Hecke operators on period functions for ${\Gamma }_0(n)$

Abstract

Matrix representations of Hecke operators on classical holomorphical cusp forms and the corresponding period polynomials are well known. In this article we derive representations of Hecke operators for vector valued period functions for the congruence subgroups ${\Gamma }_0(n)$. For this we use an integral transform from the space of vector valued cusp forms to the space of vector valued period functions.

v2: corrected version, submitted to Journal of Number, 29 pages, 1 figure