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