ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 04 Aug 2015 08:05:56 -0500Approximating Periods of Modular Symbols on Weight Two Modular Formshttps://ask.sagemath.org/question/28721/approximating-periods-of-modular-symbols-on-weight-two-modular-forms/A modular symbol corresponds to an element of homology on a modular curve (relative to the cusps) and a weight two modular form corresponds to a holomorphic one-form. Given a modular symbol and a weight two modular form, how can I approximate the integral of the modular form over the relative cycle corresponding to the modular symbol?
An example (which fails to work) is the following:
f = Newforms(Gamma0(23), 2, names='a')[0];
M = ModularSymbols(23,2);
H = M.basis();
gamma = H[0];
f.period(gamma)Wed, 29 Jul 2015 18:28:14 -0500https://ask.sagemath.org/question/28721/approximating-periods-of-modular-symbols-on-weight-two-modular-forms/Comment by vdelecroix for <p>A modular symbol corresponds to an element of homology on a modular curve (relative to the cusps) and a weight two modular form corresponds to a holomorphic one-form. Given a modular symbol and a weight two modular form, how can I approximate the integral of the modular form over the relative cycle corresponding to the modular symbol?</p>
<p>An example (which fails to work) is the following:</p>
<pre><code>f = Newforms(Gamma0(23), 2, names='a')[0];
M = ModularSymbols(23,2);
H = M.basis();
gamma = H[0];
f.period(gamma)
</code></pre>
https://ask.sagemath.org/question/28721/approximating-periods-of-modular-symbols-on-weight-two-modular-forms/?comment=28756#post-id-28756see also [this thread on sage-support](https://groups.google.com/forum/#!topic/sage-support/1Wj5m22xY6E)Tue, 04 Aug 2015 08:05:56 -0500https://ask.sagemath.org/question/28721/approximating-periods-of-modular-symbols-on-weight-two-modular-forms/?comment=28756#post-id-28756