A Generalization of Level-Raising Congruences for Algebraic Modular Forms

Abstract

In this paper we prove a general theorem about congruences between automorphic forms on a reductive group G which is compact at infinity modulo the center. If the rank is one, this essentially reduces to Ribet's level-raising theorem. We then specialize to the higher rank case where G is an inner form of GSp(4). Here we get congruences with automorphic forms having a generic local component. In particular, a Saito-Kurokawa form is congruent to a form which is not of Saito-Kurokawa type. We get similar results for U(3) at split primes.