#9455: Dimensions of eigenspaces for the Atkin-Lehner operator acting on modular
forms
-------------------------+-------------------------------------------------
Reporter: ljpk | Owner: craigcitro
Type: | Status: needs_work
enhancement | Milestone: sage-6.9
Priority: minor | Resolution:
Component: | Merged in:
modular forms | Reviewers:
Keywords: atkin | Work issues:
lehner | Commit:
Authors: Lloyd | 311782f16080ea75c9cef9671d92b50a6f570785
Kilford | Stopgaps:
Report Upstream: N/A |
Branch: |
u/chapoton/9455 |
Dependencies: |
-------------------------+-------------------------------------------------
Changes (by davidloeffler):
* status: needs_review => needs_work
Comment:
This needs some serious work.
- Most of this new code is added via methods of Gamma0 modular forms space
objects. However, these objects can have any weight, but the
implementations here only work for weight 2, so you can type something
like
{{{
sage: ModularForms(1000003, 4).atkin_lehner_eigenspace_dimensions()
}}}
and it will silently return wrong output. More importantly, lots of these
methods (e.g. {{{atkin_lehner_ramification}}}) are computing geometric
properties of the underlying modular curves, so they belong in
{{{sage.modular.arithgroup.congroup_gamma0}}}. Similarly,
"primitive_ideal_number" should probably be a method of order objects, not
a standalone function.
- Many function names are mysterious or downright misleading, e.g. the
method {{{modular_genus_X0}}} is not actually computing the genus of
anything in most cases.
- The documentation is poor. What on earth is the "(M, R)-old subspace"?
What are "cyclic ideals"? Docstrings for each method should explain what
the arguments mean. The docstring for {{{old_subspace_dimension(self, M,
R, w)}}} does not even mention Atkin--Lehner involutions!
- Why is a line of code in the number fields module (in
{{{absolute_order_from_module_generators}}}) deleted without explanation?
--
Ticket URL: <http://trac.sagemath.org/ticket/9455#comment:25>
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