#5648: [with patch, needs review] Multiplication for modular forms
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Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: minor | Milestone: sage-3.4.2
Component: modular forms | Keywords:
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Comment(by davidloeffler):
The function sturm_bound in sage.modular.dims is returning ceil( weight *
index / 12), which is the Sturm bound for M_k(Gamma) according to theorem
9.18 in your book; so it should be fine for Eisenstein series.
(In fact, sage.modular.dims.sturm_bound for GammaH and Gamma1 is actually
doing something a bit strange -- it calculates the Sturm bound for the
corresponding Gamma0 and multiplies it by the index of the given group in
Gamma0, so it is giving a wastefully high bound due to premature rounding.
I noticed this, and fixed it, as part of #5180.)
Ideally ModularForms(N, k).sturm_bound() and CuspForms(N, k).sturm_bound()
should return different answers corresponding to the two statements in
your theorem 9.18, in order to be really painfully efficient with not
computing more terms than we need. Furthermore ModularForms(character,
k).sturm_bound() should return the Buzzard-Sturm bound for forms of known
character. (I think I might have already put the latter in #5180). But all
this is optimisation; it should work fine as-is.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5648#comment:3>
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