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Database halfintegralmf
Description Half integral weight cuspforms spaces and Shimura decomposition
Status alpha
Contact Samuele Anni
Code half_integral_weight_forms
Collections forms

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)

Collection forms

  • character (string): character label in the LMFDB notation
  • dim (int): dimension of the space
  • dimtheta (int): dimension of the S0 subspace (see the shimura decomposition knowl here)
  • label (string): LMFDB label
  • level (int): Level
  • newpart (list of dictionaries): 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 (list of strings): label of the characters appearing in the S0 subspace
  • weight (int): double of the weight of the forms

LMFDB label of an Half Integral Weight Cuspforms spaces

The LMFDB label has the following structure:

level.weight_2.character_label

One example of forms

{u'_id': ObjectId('55b9c5f7ffe9794ba58d8925'),
u'character': u'1.1',
u'dim': 5,
u'dimtheta': 1,
u'label': u'108.3_2.1.1',
u'level': 108,
u'newpart': [{u'dim_image': 2,
  u'half_forms': [[u'1',
    u'0',
    u'0',
    u'0',
    u'0',
    u'0',
    u'1',
    u'0',
    u'0',
    u'-2',
    u'0'],
   [u'0', u'0', u'0', u'1', u'0', u'0', u'-1', u'0', u'0', u'0', u'0']],
  u'mf_label': u'27.2a',
  u'nf_label': u'1.1.1.1'},
 {u'dim_image': 1,
  u'half_forms': [[u'1',
    u'-1',
    u'0',
    u'1',
    u'3',
    u'0',
    u'-1',
    u'-1',
    u'0',
    u'-3',
    u'-3']],
  u'mf_label': u'54.2a',
  u'nf_label': u'1.1.1.1'},
 {u'dim_image': 1,
  u'half_forms': [[u'0',
    u'0',
    u'1',
    u'0',
    u'0',
    u'-1',
    u'0',
    u'0',
    u'1',
    u'0',
    u'0',
    u'-1']],
  u'mf_label': u'54.2b',
  u'nf_label': u'1.1.1.1'}],
u'thetas': [[u'3.2']],
u'weight': 3}