#12043: Hecke series for overconvergent modular forms
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Reporter: lauder | Owner: craigcitro
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: modular forms | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: David Loeffler
Authors: Alan Lauder | Merged in:
Dependencies: | Stopgaps:
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Comment (by davidloeffler):
Here's what I get with all my optimizations:
{{{
sage: time hecke_series(p = 59, N = 1, klist = 2, m = 5)
690689577*x^10 + 227559932*x^9 + 426975979*x^8 + 473462905*x^7 +
665599061*x^6 + 356193732*x^5 + 408559793*x^4 + 585093835*x^3 +
432796757*x^2 + 22614222*x + 1
Time: CPU 1.34 s, Wall: 1.52 s
}}}
So the Sage implementation has pulled ahead of the Magma one now, at least
for these level 1 cases.
I think there is only one more thing we need to do, if we're willing to
live with the unproven conjecture about weights of generators. That is, to
modify the !ModularFormsRing code so the generators it returns are
''always'' integral, and so that the ZZ-submodule they generate is
saturated in weights up to the given bound. This is not too hard to do --
I already have code that does it, I just need to merge it into the Sage
library. Then I think we can get this in (modulo yourself or someone else
reviewing my contributions). I'm not saying that there isn't room for
further optimizations, but those can come in subsequent tickets.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12043#comment:17>
Sage <http://www.sagemath.org>
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