Cuspidal modular symbols are transportable

William A. Stein and Helena Verrill

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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