Hecke polynomial of a cusp form space is needlessly slow

[kedlaya]

Reported by bober on sage-nt, see ​https://groups.google.com/forum/#!topic/sage-nt/AbtJF3Z5_fM.

sage: S = CuspForms(1728, 2)
sage: %time f = S.hecke_polynomial(2)
CPU times: user 17276.68 s, sys: 13.46 s, total: 17290.14 s
Wall time: 17293.59 s
sage: f
x^253 + x^251 - 2*x^249

Meanwhile, in a separate Sage session...

sage: %time M = ModularSymbols(1728, 2, 1)
CPU times: user 0.47 s, sys: 0.03 s, total: 0.50 s
Wall time: 0.54 s
sage: %time S = M.cuspidal_subspace()
CPU times: user 1.57 s, sys: 0.00 s, total: 1.57 s
Wall time: 1.54 s
sage: %time f = S.hecke_polynomial(2)
CPU times: user 19.09 s, sys: 0.00 s, total: 19.09 s
Wall time: 19.07 s
sage: f
x^253 + x^251 - 2*x^249

[davidloeffler]

I fixed this at the same time as fixing #24300. Please review that ticket. Once it's reviewed and merged this can be closed.

[vdelecroix]

Would be cool to have a doctest. That is a test that would take hours before but take reasonable amount after #24300.

[davidloeffler]

OK, I've put the example from the bug report as a doctest. The new code gets it down from 4.5 hours to 20 seconds, but it's still on the long side for a doctest so I've flagged it with # long time.

---

New commits:

​099ae38	Trac 24300: speed up computation of modular form Hecke matrices
​9424b1f	Trac 24300: fix deprecated ReST syntax
​fe985bc	Trac 24300: extra doctests requested by reviewer

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​51d0cc8

Trac 21546: add doctest (to show that problem is fixed by #24300)

[davidloeffler]

Oops, forgot to commit before I pushed!