#9455: Dimensions of eigenspaces for the Atkin-Lehner operator acting on modular
forms
---------------------------------+---------------------------
Reporter: ljpk | Owner: craigcitro
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.11
Component: modular forms | Resolution:
Keywords: | Merged in:
Authors: ljpk | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Description changed by chapoton:
Old description:
> This is a port of David Kohel's MAGMA code to compute dimensions of the
> eigenspaces for the Atkin-Lehner operators acting on spaces of cusp forms
> of weight 2 (see here for the original):
>
> http://echidna.maths.usyd.edu.au/echidna/dbs/atkin-lehner/index.html
>
> These methods do not rely on computing explicit bases of newforms,
> instead using formulae about the ramification points of the Atkin-Lehner
> operator.
>
> These functions use the class number method qfbclassno() from Pari/GP.
>
> NOTES: the functions for newforms are really slow right now (much slower
> than MAGMA).
>
> The public methods supplied here are:
>
> {{{def modular_genusX0(self,w):
> def atkin_lehner_eigenspace_dimensions(self):
> def new_subspace_dimensionX0(self):
> def atkin_lehner_new_eigenspace_dimension(self,w):
> def old_subspace_dimension(self,M,R,w):
> def atkin_lehner_new_eigenspace_dimensions(self):
> }}}
> Is this too many? the most important two are
> atkin_lehner_eigenspace_dimensions and
> atkin_lehner_new_eigenspace_dimension as those give the really important
> data about spaces of modular forms. We could make the others private if
> we wanted to and not lose (too) much.
New description:
This is a port of David Kohel's MAGMA code to compute dimensions of the
eigenspaces for the Atkin-Lehner operators acting on spaces of cusp forms
of weight 2 (see here for the original):
http://echidna.maths.usyd.edu.au/echidna/dbs/atkin-lehner/index.html
These methods do not rely on computing explicit bases of newforms, instead
using formulae about the ramification points of the Atkin-Lehner operator.
These functions use the class number method qfbclassno() from Pari/GP.
NOTES: the functions for newforms are really slow right now (much slower
than MAGMA).
The public methods supplied here are:
{{{
def modular_genusX0(self,w):
def atkin_lehner_eigenspace_dimensions(self):
def new_subspace_dimensionX0(self):
def atkin_lehner_new_eigenspace_dimension(self,w):
def old_subspace_dimension(self,M,R,w):
def atkin_lehner_new_eigenspace_dimensions(self):
}}}
Is this too many? the most important two are
atkin_lehner_eigenspace_dimensions and
atkin_lehner_new_eigenspace_dimension as those give the really important
data about spaces of modular forms. We could make the others private if we
wanted to and not lose (too) much.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/9455#comment:5>
Sage <http://www.sagemath.org>
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