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halfintegralmf.forms.adoc

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Database report for halfintegralmf\forms

Prepared with the lmfdb asciidoc report tool

Christopher Brady <[email protected]>

Version 1.0.0

Collection information

Description

Half integral weight cuspforms spaces and Shimura decomposition

Status

Contact

Code

List of keys in the database

The following keys appear in at least one record in the database

Warning

The type of the keys is inferred from only one record in the database. If the key can have different types in different records this type will be inaccurate Only the first 100 characters of the example record are shown
Key Inferred Type Example record Description

character

real stored as string

1.1

character label in the LMFDB notation

dim

integer

5

dimension of the space

dimtheta

integer

1

dimension of the S0 subspace (see the shimura decomposition knowl here)

label

string

108.3_2.1.1

LMFDB label

level

integer

28

Level

newpart

collection of mixed types

[{u’dim_image': 2, u’nf_label': u'1.1.1.1', u’half_forms': [[u'1', u'0', u'0', u'0', u'0', u'0', u'1 …​

description of the subspace corresponding to the image of the shimura map. The entries of the dictionary contain the following fields:

  • dim_image (int) the dimension of the subspace given by the image

  • half_forms (list of lists of strings) the coefficients (algebraic integers) of the q-expansions of the half integral weight newforms in the image

  • mf_label (string) the label of the classical newform which is mapped into this space of half integral weight cuspforms

  • nf_label (string) the label of the number field where the coefficients of the q-expansion belong to (this will be changed into the list of coefficients of a polynomial)

thetas

collection of real stored as string

[[u'3.2']]

label of the characters appearing in the S0 subspace

weight

integer

3

double of the weight of the forms

List of indices

Index Name Index fields

id

_id sorted ascending

level_1_label_1

level sorted ascending, label sorted ascending

metadata_1

metadata sorted ascending

List of record types in the database

All records

Note

3 records of type

  • character

  • dim

  • dimtheta

  • label

  • level

  • newpart

  • thetas

  • weight

Notes

Comments: Work in progress, check the branch half_integral on https://github.com/sanni85/lmfdb.git for the latest.

Data will be uploaded from here.

Todo: add index information for forms correct all the labels of classical newforms stored (since they changed in the last update)