Abstract

We study several methods for the numerical computation of Petersson scalar products, and in particular we prove a generalization of Haberland’s formula to any subgroup of finite index $G$ of $\Gamma ={PSL}_{\mathfrak{2}}\left(\mathbb{Z}\right)$, which gives a fast method to compute these scalar products when a Hecke eigenbasis is not necessarily available.

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Mathematical Subject Classification 2010

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