Opened 3 years ago

Last modified 2 years ago

#19774 needs_work enhancement

Full support for modular forms for the Theta subgroup

Reported by: jj Owned by:
Priority: major Milestone: sage-7.0
Component: modular forms Keywords: modular forms theta subgroup half-integer weight
Cc: mraum Merged in:
Authors: Jonas Jermann Reviewers:
Report Upstream: N/A Work issues:
Branch: u/jj/theta_space (Commits) Commit: b3508cba62e714ccaea1cdaba6d22dd5855eb172
Dependencies: #17909 Stopgaps:

Description (last modified by jj)

The current implementation of modular forms for the Theta subgroup only allows modular forms with integer orders at the cusp -1. With this ticket all forms are supported, also forms with fractional order at the cusp -1. In particular this includes the theta function / half-integer weight forms.

Also note that there is a correspondence between modular forms for the Theta subgroup and modular forms for Gamma0(4). So in essence this ticket provides support for classical half-integer weight modular forms (for Gamma0(4)) for all kind of analytic types: cuspidal, holomorphic, weakly holomorphic, meromorphic and also quasi forms, as ring or module elements and with a lot of powerful methods.

The ticket depends on the branch u/jj/rankin_cohen_bracket (#17909).

The ticket is essentially implemented.

Possible additional ideas:

  • Kohnen plus spaces
  • Eisenstein series
  • basis/detection of forms for the direct sum for ep=1 and ep=-1 (which corresponds to the Modularform space for Gamma0(4)).

Change History (4)

comment:1 Changed 3 years ago by git

  • Commit changed from d6c377f55e1b37bbc9f794bdc7a719591b8a9c8c to 39d895b7826533c97fc76e56238fb6cd3e34f860

Branch pushed to git repo; I updated commit sha1. New commits:

39d895bminor bugfixes, more documentation

comment:2 Changed 3 years ago by git

  • Commit changed from 39d895b7826533c97fc76e56238fb6cd3e34f860 to b3508cba62e714ccaea1cdaba6d22dd5855eb172

Branch pushed to git repo; I updated commit sha1. New commits:

b3508cbsome more background information

comment:3 Changed 3 years ago by jj

  • Description modified (diff)
  • Status changed from new to needs_review

comment:4 Changed 2 years ago by cheuberg

  • Status changed from needs_review to needs_work

The branch no longer merges with current sage releases.

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