Approximating Periods of Modular Symbols on Weight Two Modular Forms

asked 2015-07-30 01:28:14 +0200

Paul Apisa gravatar image

updated 2015-08-04 14:04:43 +0200

slelievre gravatar image

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];
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vdelecroix gravatar imagevdelecroix ( 2015-08-04 15:05:56 +0200 )edit