Ticket #12740 (closed enhancement: fixed)
Revamp code for finding generators of modular forms spaces
|Reported by:||davidloeffler||Owned by:||craigcitro|
|Report Upstream:||N/A||Reviewers:||Jan Vonk|
|Authors:||David Loeffler||Merged in:||sage-5.1.beta2|
The module sage.modular.modform.find_generators contains code which calculates, for a given congruence subgroup, forms which generate the graded ring of modular forms of that level; and code which uses these generators to calculate bases of q-expansions for spaces of very large weight, where modular symbol computations are less efficient.
This code is old and has not been very actively maintained for some while. Motivated by #12043, which uses this code, I decided to rework it a bit. With the attached patch, the new code
- uses a randomized algorithm in some cases, adapted from Alan Lauder's code at #12043
- can work over arbitrary base rings (not just the rationals)
- handles series precision a bit more cleverly, using Sturm's bound
- can now calculate generators for the ideal of cuspidal forms, and thus bases of q-expansions of large weight cuspidal submodules.
- Status changed from needs_review to positive_review
- Reviewers set to Jan Vonk