#6072: Boundary space for GammaH fails to identify vanishing classes
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: new
Priority: minor | Milestone: sage-4.0.1
Component: modular forms | Keywords:
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If G is a congruence subgroup (not containing -1), then cusps of G can
"magically" vanish in the space of odd weight boundary symbols when the
weight is odd.
Reading the explanation in boundary.py, I think that the explanation there
just boils down to that this happens if and only if the cusp is irregular
(in the sense that the generator of its stabiliser looks like [-1, h ; 0,
-1]). But for the group {{{GammaH(8, [3])}}} there are 4 cusps of which 2
are irregular, namely 1/2 and 1/4 -- but the boundary space doesn't
realise this. It's possible that I've misunderstood the definitions, but
I'm pretty sure that the boundary space is supposed to be dual to the
space of Eisenstein series, and that certainly has dimension 2 here.
This is certainly of no great significance at the moment since we don't
really have much functionality working for GammaH spaces anyway, but it's
still not ideal that the functionality we do have implemented is giving
wrong answers.
Craig: I'm ccing you here as I got the impression you wrote most of the
GammaH stuff -- do you have any idea what's going on here?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6072>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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