# Cuspidal modular symbols are transportable

**Abstract**

Modular symbols of weight 2 for a congruence subgroup Gamma satisfy
the identity {alpha, gamma(alpha)} = {beta,gamma(beta)} for all alpha,
beta in the upper half plane and gamma in Gamma. The analogue of this
identity is false for modular symbols of weight greater than 2. In
this paper we define transportable modular symbols, which are symbols
for which the above identity holds, and prove that every cuspidal
symbol can be written as a transportable symbol. As a corollary we
obtain an algorithm for computing periods of cuspforms.

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