Relations between cusp forms sharing Hecke eigenvalues

Abstract

In this paper we consider the question of when the set of Hecke eigenvalues of a cusp form on G L n ( A F ) GL_n(\mathbb {A}_F) is contained in the set of Hecke eigenvalues of a cusp form on G L m ( A F ) GL_m(\mathbb {A}_F) for n ≤ m n \leq m . This question is closely related to a question about finite dimensional representations of an abstract group, which also we consider in this work.