#19774: Full support for modular forms for the Theta subgroup
-------------------------------------+-------------------------------------
Reporter: jj | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: modular forms | Resolution:
Keywords: modular forms | Merged in:
theta subgroup half-integer | Reviewers:
weight | Work issues:
Authors: Jonas Jermann | Commit:
Report Upstream: N/A | b3508cba62e714ccaea1cdaba6d22dd5855eb172
Branch: u/jj/theta_space | Stopgaps:
Dependencies: #17909 |
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Changes (by jj):
* status: new => needs_review
Old description:
> 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 basically implemented but some more testing/documentations
> are required.
New description:
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)).
--
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Ticket URL: <http://trac.sagemath.org/ticket/19774#comment:3>
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