2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227585The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.30 pages; corrected typos and fixed incomplete proofs in section 3Number Theory11F25, 11F67 (Primary); 37C30, 37D20, 81Q50 (Secondary)text