#16883: Modular forms for the theta subgroup (as part of Hecke triangle groups)
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Reporter: jj | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: modular forms | Keywords: theta subgroup
Merged in: | modular forms hecke triangle
Reviewers: | Authors: Jonas Jermann
Work issues: | Report Upstream: N/A
Commit: | Branch: u/jj/theta_group
988bdadce2f5a50af09f8b7a668c3e9e4f7a6a46| Dependencies: 16839
Stopgaps: |
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Support for modular forms for the Hecke triangle group corresponding to
n=infinity
(the theta subgroup). All relevant spaces are defined and the basic
generators/functions work.
Laurent expansions, (fast) function evaluation and differential operators
work.
The ticket also adds corresponding + further doctests/documentation.
However no basis can be generated so far and no coordinate vectors work.
That's because the situation is different since there are now two cusps
with
two corresponding generators.
In particular the limit of the generator f_rho tends to 1 and the
generator
for n=infinity is instead E4 which is the limit of f_rho^n.
Note that only functions which are meromorphic and meromorphic at the
cusps are considerd.
In particular theta^8 lies in the corresponding space (smaller powers are
not meromorphic at -1).
Also note that limits of functions/coefficients as n tends to infinity are
usually given by
the corresponding function in the theta subgroup.
--
Ticket URL: <http://trac.sagemath.org/ticket/16883>
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