Full support for modular forms for the Theta subgroup

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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)).

Depends on #17909

CC: @sagetrac-mraum

Component: modular forms

Keywords: modular forms theta subgroup half-integer weight

Author: Jonas Jermann

Branch/Commit: u/jj/theta_space @ b3508cb

Issue created by migration from https://trac.sagemath.org/ticket/19774

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from d6c377f to 39d895b

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

39d895b

minor bugfixes, more documentation

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

b3508cb

some more background information

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 39d895b to b3508cb

[a1dd0ea6-9300-4f97-bb3c-0f25ba420caf]

Description changed:

--- 
+++ 
@@ -11,4 +11,10 @@

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

-The ticket is basically implemented but some more testing/documentations are required.
+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)).

[cheuberg]

comment:4

The branch no longer merges with current sage releases.