A generalization of Ramanujan's congruence to modular forms of prime level

Radu Gaba, Alexandru A. Popa

Published 2016-12-02Version 1

We prove congruences between cuspidal newforms of prime level and Eisenstein series, which generalize Ramanujan's congruence modulo 691. For the proof, we study the new subspace and the Eisenstein subspace of the space of period polynomials for the congruence subgroup $\Gamma_0(N)$. We also prove a version of Ihara's lemma, previously used to prove congruences between cusp forms.