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All collections contain the field _id which is an object of the type bson.ObjectId and uniquely identifies the record in the database.
All collections with names ending with .chunks contain chunks of files for GridFS for the corresponding collection with name ending with .files and will not be further described.
All collections with names ending with .files contain data for GridFS files and will (or at least should) all contain the following fields (which will not be repeted below except 'filename' which has a different format in each collection):
The dimension of the space of Eisenstein series E_k(Gamma_1(N))
d_mod
integer
189
The dimension of the space of all modular forms M_k(Gamma_1(N))
d_newf
integer
integer
161
gamma1_label
string
'29.6'
A label for the space, of the form level.weight
all_in_db
bool
True
True if the spaces S_k^{new}(N,chi) for all chi are in the db, False otherwise
one_in_wdb
bool
True
True if at least one of these spaces is in the db
Gamma0 with character
Field
type
Example
Description
cchi
integer
9
Conrey character number
character_orbit
list
[9, 11]
List of conrey character numbers of elements of the orbits of 'cchi'
character_orbit_rep
integer
9
The number of the representative of the Galois orbit
character_parity
integer
1
'1' if the character is even and '-1' if it is odd
d_cusp
integer
24
Dimension of space of cusp forms S_k(N, chi), where N is the level, chi is the character specified by cchi.
d_eis
integer
4
Dimension of Eisenstein series E_k(N,chi)
d_mod
integer
28
Dimension of modular forms M_k(N,chi)
d_newf
integer
8
Dimension of (cuspidal) newforms in S_k(N,chi)
in_msdb
integer
1
Equals 1 if this space has a record in the Modular_Symbols.files collection, else 0
in_wdb
integer
1
is 1 if we have this space in the web database, i.e. an entry exists in the collection webmodformspace and all galois orbits of newforms are stored in the collection webnewforms, else 0
level
integer
14
The level of the space
space_label
string
'14.14.9'
the label of this space of the form N.k.i where N is the level, k the weight and i the Conrey character number
space_orbit_label
string
'14.14.2'
The label of the Galois orbit of this space of the form N.k.i, where i is the index of the Galois orbit of the character in the list of Galois orbits of characters of this level. The Galois orbits are ordered by the minimal number appearing in the orbit.
weight
integer
14
the weight of self
collection webmodformspace_dimension
Description: more dimension data for webmodform spaces
Field
type
Example
Description
`weight_max` | integer | 100 | the largest weight in the table
`group` | string | u'gamma0' | the group, either 'gamma0' or 'gamma1'
`level_max` | integer | 100 | the maximum level contained in this table
`date` | datetime | datetime.datetime(2016, 5, 4, 17, 33, 55, 54000) | when this dimension data was generated
`data` | string | "{'1' : {'12' : [1,1] }}" | unicode string giving json formatted dimension data in the form data[level][weight]=[d,i] where d is the dimension and i=1 if this space is in the database and otherwise 0
Collection webchar
Description: Json data for WebCharacter objects as defined in '/modular_forms/elliptic_modular_forms/backend/web_character.py'
Field
type
Example
Description
conductor
integer
1
conductor
label:
string
'1.1'
label of the form M.i where M is the modulus and i is the Conrey character number
latex_name:
string
'\chi_{1}(1, \cdot)'
latex_string
modulus
integer
1
modulus
modulus_euler_phi
integer
1
Euler phi function of modulus
number
integer
1
Conrey character number
order
integer
1
order of this character
version
float
1.2
version number
Collection webchar.files
Description: GridFS files associated with WebCharacter objects.
Field
type
Example
Description
modulus
integer
3
modulus of the character
number
integer
1
Conrey character number
Collection webmodformspace
Description: Json data for a Modular form space object of type 'WebModFormSpace' defined in /modular_forms/elliptic_modular_forms/backend/web_modform_space.py
Field
type
Example
Description
_has_oldspace
integer
0
1 if we have computed the decomposiiton of the space of oldforms, else 0
bitprec
integer
53
the precision (in bits) of the stored embedded coefficients default is 53 = double precision
character
integer
1
number of the character
character_naming_scheme
string
`Conrey'
'Conrey' or 'Sage', used to denote the naming/labeling scheme used. Default is 'Conrey'
character_orbit_rep
integer
1
The number of the character which is the representative of the Galois orbit (in the same naming scheme as above). The representative is chosen as the smallest integer in the list of character numbers
character_used_in_computation
integer
1
number of the character which was used in the computation (could be another character in the Galois orbit)
creation_date
datetime
datetime.datetime(1970, 1, 1, 0, 0)
when the record was created
cuspidal
integer
1
1 if the record describes a space of cusp forms, else 0
dimension
integer
0
dimension of this space
dimension_cusp_forms
integer
0
dimension of the space of cusp forms with this level, weight and character
dimension_modular_forms
integer
1
dimension of the space of modular forms with this level, weight and character
dimension_new_cusp_forms
integer
0
dimension of the space of (cuspidal) newforms with this level, weight and character
hecke_orbits
list
[]
list of labels of the newforms Hecke orbits of self which are stored in the collection 'webnewforms'
level
integer
2
level
prec
integer
10
number of coefficients stored in the q-expansions for the newforms (if they are stored)
space_label
string
`2.2.1'
label of the format level.weight.character where character is the number above (in particular given by the naming scheme in 'character_naming_scheme')
space_orbit_label
string
`2.2.0'
label of the format level.weight.o where o is the number of the galois orbit of the character in the list of all galois orbits (ordered by their minimal element)
sturm_bound
integer
0
the Sturm bound for this space, i.e. a general bound on the number of coefficients which must be given to uniquely indentify a modular form in this space
version
float
1.2
version number
weight
integer
2
weight
zeta_orders
list
[]
list of orders of the generators of the cyclotomic fields which are the base fields of the Fourier coefficients of the newforms in the database
Collection webmodformspace.files
Description: GridFS files associated with WebModFormSpace objects which are also given by records in the collection webmodformspace. See the definition of 'WebModFormSpace' in /modular_forms/elliptic_modular_forms/backend/web_modform_space.py
File format: a dictionary containing data for the webmodformspace as described in the second table below.
Field
type
Example
Description
space_label
string
'10.8.7'
label of the form level.weight.character corresponding to the record in the collection 'webmodformspace'
version
float
version number
Data structure for the file
Field
type
Example
Description
_character_galois_orbit
list
[1]
list of characters in the Galois orbit of the character
_character_galois_orbit_embeddings
dict
{}
embeddings (if computed)
character_naming_scheme
string
'Conrey'
character naming scheme
character_orbit_rep
integer
1
the number of the representative of the Galois orbit (should be the smallest number in the orbit)
character_used_in_computation
integer
1
the character used to compute this space
group
string
'x\x9ck`J.NLO\xd5\xcb\xcdO)\xcdI,...'
a binary string givng the subgroup as an object of type sage.modular.arithgroup.congroup_gamma0.Gamma0_class_with_category
oldspace_decomposition
{}
the decomposition of the old subspace of this modular form space
space_label: '32.6.1'
the label in format level.weight.character
version
float
1.3
version number
zeta_orders
list
[]
list of orders of the generators of the cyclotomic field which the character takes values in
Collection webnewforms
Description: Json data for a Newform object of type 'WebNewform' as defined in '/modular_forms/elliptic_modular_forms/backend/web_newforms.py'
Field
type
Example
Description
absolute_polynomial
string
`x^2 - 3072'
the absolute polynomial for the coefficient field
base_ring
string
`1.1.1.1'
the base field of the coefficient field. Should be the same as the field in which the character has values (we view the trivial character as having values in Q which has label '1.1.1.1')
character
integer
1
the character number in the scheme described below
character_naming_scheme
string
`Conrey'
The naming scheme of the character used for this object
cm_disc
integer
0
equals D, the discriminant of the imaginary quadratic field with which this newform has CM if it has CM, else 0
coefficient_field
string
`2.2.12.1'
the label (in the format as given by lmfdb number fields) of the coefficient field
coefficient_field_degree
integer
2
the absolute degree of the coefficient field
creation_date
datetime datetime.datetime(2016, 4, 13, 9, 43)
when this record was created
dimension
integer
2
dimension of this newform as an irreducible submodule of the ambient space
hecke_orbit_label
string
'32.6.1.d'
the label of format level.weight.character.label where 'label' is given in the field label below
is_cm
integer
0
1 if this newform has CM, else 0
is_cuspidal
integer
1
1 if this record corresponds to a cuspidal newform (for future compatibility if Eisenstein series will be included), else 0
is_rational
integer
0
1 if this newform has rational Fourier coefficients, else 0
label
`d'
label of this orbit in the 'Cremona label' convention, i.e. the first (0th in python ordering) orbit has label 'a', the second 'b', the 27-th 'aa' and then 'ab', the 702nd is 'aaa' etc.
level
integer
32
level
modification_date
datetime
datetime.datetime(2016, 4, 13, 9, 43, 44, 974000)
when this record was last modified
parent
`32.6.1'
label of form label.weight.character of the space which contains the given newform (corresponding to the key 'space_label' in the collection webmodformspace)
prec
integer
190
number of coefficients in the stored q-expansion (either in this record or in the gridfs record)
q_expansion
string
'q + 1/2aq^3 + 46q^5 - 3aq^7 + 525q^9'
string formatted q-expansion of this newform (if not stored here it is taken from the gridfs object in webmodformspace.files)
version
1.3
version number
weight
integer
6
weight
Collection webnewforms.files
Description: GridFS files associated with WebNewform objects in the collection webnewforms
File format: a dictionary containing data for the webnewform as described in the second table below.
Field
type
Example
Description
hecke_orbit_label
string
'11.12.1.b'
the label of this newform, corresponds to the same entry in the collection webnewforms
prec
integer
220
the number of coefficients which are stored in this record
Data structure for the file
Field
type
Example
Description
_atkin_lehner_eigenvalues
dict
{ 2:-1 }
Atkin-Lehner eigenvalues (if they are known) corresponding to divisors of N
_cm_values
list
[]
values of self at CM-points (computed numerically)
dictionary of complex embeddings with keys 'bitprec' -- the precision of the computed embeddings, 'prec'-- the number of coefficients and 'values' -- dictionary of lists containing the embeddings
dictionary representing the base ring (field) with keys: 'base' -- the base ring this is defined over (usually QQ), 'gens'-- the name(s) of the variable(s) in the polynomial, and 'relative_polynomial' -- the relative polynomial of this number field over the base
coefficient_field
{base : 'QQ', gens : 'a', relative polynomial
a^2 - 3072}
the coefficient field in the same format as above
q_expansion
sage object
q + 1/2aq^3 + 46*q^5 +O(q^7)
q-expansion as an element of sage.rings.power_series_poly.PowerSeries_poly over the coefficient field
the first entry is True if this newform is primitive and False if it is a twist, the second entry is a list of labels of newforms which twist to this newform
version
float
1.3
version number
Collection webeigenvalues.files
Description: Contains GridFS files with Hecke aigenvalues of newforms.
The format of the file is a dictionary containing the matrix and vector E and v as returned by the method compact_system_of_eigenvalues in sage. The precise format is given in the second table below.
Field
type
Example
Description
hecke_orbit_label
string
'28.6.1.a'
label of the newform, matching the record in the collection webnewforms
prec
integer
100
the number of coefficients we can get with the eigenvalues in this file
version
float
1.3
version number
Data structure for the file
Field
type
Example
Description
E
string
''
binary string giving a matrix as a sage object
v
string
''
binary string giving a vector as a sage object
meta
dict
{'cputime': u'', 'version': u''}
metadata
Collections used for computing webobjects -- not present on the cloud database
Collection Atkin_Lehner.files
Description: GridFS files containing Atkin-Lehner eigenvalues for newforms.
File format: a string of '+' and '-' corresponding to eigenvalue 1 or -1 of W_p for p in prime_divisors(N)
Field
type
Example
Description
N
integer
17
level
cchi
integer
1
Conrey character number
chi
integer
0
Sage character number (index in DirichletGroup(N)
cputime
float
5.744359
time to compute the eigenvalues
k
integer
2
weight
newform
integer
0
index of the newform in the list of all newforms with this level, weight and character, ordered as in Sage by traces of Hecke operators (?)
sage_version:
string
'7.2'
version of sage used to compute this object
filename
string
atkin_lehner_evs- 17- 2- 0- 0
filename in gridfs
Collection Modular_symbols.files
Description: GridFS files containing modular symbols.
File format: Sage object of type 'sage.modular.modsym.ambient.ModularSymbolsAmbient_wtk_eps_with_category'
Example: Modular symbols space of dimension 75 and level 500, weight 2, character [-1, zeta4], sign 1, over Cyclotomic Field of order 4 and degree 2
Field
type
Example
Description
N
integer
500
level
cchi
integer
307
Conrey character number
character_galois_orbit
list
[307, 443]
Conrey character numbers of the orbit of cchi
chi
integer
16
sage character number
complete
integer
4
indicates how 'complete' all records for this space is, set to 4 (currently the maximum) if all newform orbits and their aps up to the bound given by the L-functions requirements are computed
conrey_galois_orbit_number
integer
16
the number of the Galois orbit in the list of all Galois orbits in DirichletGroup_Conrey
cputime
float
0.
time it took to compute this record in seconds
dima
integer
75
dimension of ambient space of modular symbols of weight k, level N, character chi and sign =-1
dimc
integer
65
dimension of cuspidal submodule
dimn
integer
48
dimension of new submodule of the cuspidal submodule
filename
string
'gamma0-ambient-modsym-00500-002-016'
filename in gridfs
k
integer
2
weight
nfactors
integer
0
number of newform factors in the database for this record (should be updated after the orbits are computed)
orbits
integer
0
same as 'nfactors' (probably one of these were introduced by some bug some time ago)
sage_version
string
'6.1beta'
version of sage used to compute the object (and that may be needed to unpickle it sucessfully)
space_label
string
'500.2.307'
label of the space in the format N.k.cchi
space_orbit_label
string
'500.2.16'
label of the orbit of the space in the format N.k.o where 'o' is the order of the Galois orbit in the list of all Galois orbits in DirichletGroup_Conrey
Collection Newform_factors.files
Description: GridFS files containing newform factors.
File format: Sage object of type 'sage.modular.modsym.subspace.ModularSymbolsSubspace_with_category'
Example: Modular symbols subspace of dimension 1 of Modular Symbols space of dimension 70 for Gamma_0(372) of weight 2 with sign 1 over Rational Field
Field
type
Example
Description
N
integer
372
level
ambient_id
string
ObjectId('56be2428769754c49d4031d5')
id of the corresponding ambient space record in Modular_symbols.files
cchi
integer
1
conrey character number
character_galois_orbit
list
[1]
chi
integer
0
sage character number
chunkSize
integer
261120
chunk size of gridfs files
conrey_galois_orbit_number
integer
0
the number of the Galois orbit in the list of all Galois orbits in DirichletGroup_Conrey
cputime
0.8625200000000002
time it took to compute this record in seconds
filename
'gamma0-factors-00001-00500/00372-002-000-002' time it took to compute this record in seconds
hecke_orbit_label
string
`372.2.1.c'
the label of the Hecke orbit in the format N.k.cchi.label where 'label' is the string representation given by 'newform' using the 'Cremona label' conventions
k
integer
2
weight
length
integer
152207
length of the file
md5
string
'19ea166976add07563e23bece2eb9458'
hash of the file
newform
integer
2
the number of the newform in the list of all newforms of level N, weight k and character cchi, ordered as in Sage (by traces of Hecke eigenvalues...)
the dual eigenvector as returned by the sage method compact_system_of_eigenvalues although this seems to be set to '1' in all records so I assume the records in 'vector_on_basis.files' or 'ap.files' should be used instead?
Collection ap.files
Description: GridFS files containing ap's.
File format: Tuple of the form (E,v) where E is an 'n times d' matrix
and v is a length d vector as returned by the method 'compact_system_of_egenvalues(primes_first_n(n))' on a newform factor (object in the GridFS collection 'Newform_factors').
Example: (25 x 4 dense matrix over Number Field in a with defining polynomial x^4 + 4*zeta12*x^2 + (4*zeta12^3 - 8*zeta12^2 - 8*zeta12 + 4)*x + 6*zeta12^2 - 10 over its base field, (1, (8/37*zeta12^3 - 109/444*zeta12^2 + 6/37*zeta12 + 5/111)*a^3 + (29/111*zeta12^3 - 5/12*zeta12^2 - 61/444*zeta12 + 1/12)*a^2 + (-83/111*zeta12^3 + 139/148*zeta12^2 + 121/444*zeta12 - 53/148)*a - 7/3*zeta12^3 - 293/222*zeta12^2 + 19/6*zeta12 - 244/111, ...))
Field
type
Example
Description
N
integer
90
level
ambient_id
ObjectId('55baa63d769754a2084cc440')
id of the ambient space in the collection Modular_Symbols.files
cchi
integer
47
Conrey character number
character_galois_orbit
[23, 47, 77, 83]
the galois orbit of cchi
chi
integer
4
sage character number
conrey_galois_orbit_number
integer
5
the number of the Galois orbit in the list of all Galois orbits in DirichletGroup_Conrey
cputime
2.290000000000001
time it took to compute this (in seconds)
filename
`gamma0-aplists-00090-002-005-001-00000-00100'
file name in gridfs
hecke_orbit_label
`90.2.47.b'
label of the Hecke orbit (see above)
k
integer
2
weight
newform
integer
1
the number of the newform in the list of all newforms with level N, weight k and character cchi
nmax
integer
100
the end prime in the list, for instance 97
nmin
integer
0
the starting prime in the list ('0' means the first prime which is 2)
prec
integer
100
the number of a(n) that can be obtained by the a(p)'s in this file
sage_version
string
`Sage Version 5.0.beta7, Release Date: 2012-03-05'
version of sage used to compute this object
Collection computations
Description: contains information about ongoing computations (however this doesn't really work as intended at the moment...)
Field
type
Example
Description
N
integer
32
level
cch
integer
31
character number in Conrey scheme
k
integer
10
weight
pid
integer
15136
process id for this computation
server
srting
u'atkin'
server name where the process is running
startTime
datetime
datetime.datetime(2016, 6, 24, 17, 6, 41, 595000)
when this computation started
type
string
'mf'
type of computation
Collection vector_on_basis.files
Description: Contains GridFS files with the vector v which describes Hecke eigenvalues of newforms. This is the vector returned by the sage method compact_system_of_eigenvalues() on an irreducible Hecke invariant subspace of the ambient space.
File format: object of the type sage.modules.free_module_element.FreeModuleElement_generic_dense
Field
type
Example
Description
N
integer
1
level
ambient_id
ObjectId
ObjectId('5232e16888aece65ecf74814')
cchi
integer
1
character number in Conrey ordering
chi
integer
0
character number in Sage ordering
filename
string
'gamma0-ambient-v-00001-036-000-000'
file name in GridFS
k
integer
36
weight
newform
integer
0
the index of the newform in the list of all newforms with level N, weight k and character cchi (starting from 0)
prec
integer
100
the number of coefficients which can be obtained from the vector in the gridfs file