#13445: Cuspidal subspace of modular forms over finite field contains forms that
are not cuspidal
-------------------------------------+-------------------------------------
Reporter: mderickx | Owner: craigcitro
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: modular forms | Resolution:
Keywords: | Merged in:
Authors: Alex Ghitza | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/AlexGhitza/ticket/13445 | cf1c1bf671fc4789308500c4805a81a35f016436
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Alex Ghitza', 'oldvalue': ''}):
* status: new => needs_review
* commit: => cf1c1bf671fc4789308500c4805a81a35f016436
* author: => Alex Ghitza
Comment:
The issue was in {{{sage.modular.modform.ambient_R.py}}}, where
{{{q_integral_basis}}} was used for positive characteristic base rings.
However, {{{q_integral_basis}}} does not guarantee that its output is in
the format exhibited by {{{q_expansion_basis}}}, i.e. starting with a
basis for the cuspidal subspace and completed to a basis of the entire
space.
The modified code now computes an integral basis for the cuspidal subspace
and then completes it to an integral basis of the whole space. This
strategy works for rings of prime power characteristic (e.g. finite fields
or integers modulo a prime power, the two main use cases currently in
Sage).
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=cf1c1bf671fc4789308500c4805a81a35f016436
cf1c1bf]||{{{fix basis of spaces of modular forms in positive
characteristic}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/13445#comment:7>
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