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### 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)

 2 No.2 Revision slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### 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(); H = M.basis();  gamma=H[0];
f.period(gamma)gamma = H[0];
f.period(gamma)