#4483: Add coefficient_field() method to ModularSymbols/ModularForms
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Reporter: jonhanke | Owner: craigcitro
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.3.1
Component: modular forms | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Changes (by AlexGhitza):
* upstream: => N/A
Old description:
> ## Define a newform (up to conjugation)
> `time nf =
> ModularSymbols(100,2,1).cuspidal_subspace().new_subspace().decomposition()[0]`
>
> `nf.coefficient_field()` -- should return the field of definition of the
> newform. (This appears to be accomplished with
> `nf.eigenvalue(1).parent()`. It would be nice to know that this really
> does give the field of definition.)
>
> `nf.degree()` -- should return the degree of the coefficient field.
New description:
Define a newform (up to conjugation)
{{{
time nf =
ModularSymbols(100,2,1).cuspidal_subspace().new_subspace().decomposition()[0]
}}}
`nf.coefficient_field()` -- should return the field of definition of the
newform. (This appears to be accomplished with
`nf.eigenvalue(1).parent()`. It would be nice to know that this really
does give the field of definition.)
`nf.degree()` -- should return the degree of the coefficient field.
--
Comment:
There is something like this in Sage: look at the class {{{Newform}}} in
modular/modform/element.py. It has a method
{{{hecke_eigenvalue_field()}}} which returns the field of definition of
the newform. There is no {{{degree()}}} method, although that's of course
easy to get at this point as {{{nf.hecke_eigenvalue_field().degree()}}}.
It remains to add such a method to modular symbols
({{{nf.eigenvalue(1).parent()}}} is indeed correct), and maybe make
{{{coefficient_field()}}} an alias for {{{hecke_eigenvalue_field()}}}.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4483#comment:1>
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