#12740: Revamp code for finding generators of modular forms spaces
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Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: modular forms | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: David Loeffler
Merged in: | Dependencies:
Stopgaps: |
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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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12740>
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