Congruences for Hecke eigenvalues in minus spaces

Abstract

The minus space M-k(!) (p) is defined to be the subspace of the space M-k(!) (p) of weakly holomorphic weight k modular forms for Gamma(0)(p) consisting of all eigenforms of the Fricke involution W-p with eigenvalue -1. In this paper, we study congruences for Hecke eigenvalues in minus spaces. This is extended results for Choi and Kim (2011) [5]. We also find congruence relations satisfied by the Fourier coefficients of normalized Hecke eigenforms by extending the results of Choi and Kim (2015) [7] to the minus space. (C) 2020 Published by Elsevier Inc.