#19169: Create has_cm() function for modular forms
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Reporter: jlang | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.9
Component: modular forms | Resolution:
Keywords: modular form, cm, complex | Merged in:
multiplication, sd69 | Reviewers:
Authors: Jaclyn Lang, Amy Feaver, | Work issues:
Lubjana Beshaj, Michelle Kovesi | Commit:
Report Upstream: N/A | Stopgaps:
Branch: |
Dependencies: |
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Changes (by {'newvalue': u'Jaclyn Lang, Amy Feaver, Lubjana Beshaj, Michelle
Kovesi', 'oldvalue': u'Jaclyn Lang, Amy Feaver, Lubjana Beshaj'}):
* keywords: modular form, cm, sd69 => modular form, cm, complex
multiplication, sd69
* author: Jaclyn Lang, Amy Feaver, Lubjana Beshaj => Jaclyn Lang, Amy
Feaver, Lubjana Beshaj, Michelle Kovesi
Old description:
> A modular form $f$ has complex multiplication (cm) if there is a
> quadratic character $\epsilon$ such that
> \[
> a_p(f) = \epsilon a_p(f)
> \]
> for all but finitely many primes $p$ (those dividing the level of $f$).
> (Here, $a_p(f$) are the Fourier coefficients of $f$.) This patch creates
> a method for the modular forms class in Sage to test whether a given
> modular form has cm.
New description:
A modular form f has complex multiplication (cm) if there is a quadratic
character \epsilon such that
a(p,f) = \epsilon(p)*a(p,f)
for all but finitely many primes p (those dividing the level of f).
(Here, a(p,f) are the Fourier coefficients of f.) This patch creates a
method for the modular forms class in Sage to test whether a given modular
form has cm.
I will post code shortly.
--
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Ticket URL: <http://trac.sagemath.org/ticket/19169#comment:1>
Sage <http://www.sagemath.org>
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