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:  sage7.0 
Component:  modular forms  Keywords:  modular forms theta subgroup halfinteger 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 )
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 / halfinteger 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 halfinteger 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
 Commit changed from d6c377f55e1b37bbc9f794bdc7a719591b8a9c8c to 39d895b7826533c97fc76e56238fb6cd3e34f860
comment:2 Changed 3 years ago by
 Commit changed from 39d895b7826533c97fc76e56238fb6cd3e34f860 to b3508cba62e714ccaea1cdaba6d22dd5855eb172
Branch pushed to git repo; I updated commit sha1. New commits:
b3508cb  some more background information

comment:3 Changed 3 years ago by
 Description modified (diff)
 Status changed from new to needs_review
comment:4 Changed 2 years ago by
 Status changed from needs_review to needs_work
The branch no longer merges with current sage releases.
Branch pushed to git repo; I updated commit sha1. New commits:
minor bugfixes, more documentation