A Generalization of Level-Raising Congruences for Algebraic Modular Forms

2005/04/15 by Sorensen, Claus Mazanti
#11F33 #11F70 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0504332

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.

Related

• On Level-Raising Congruences
• Congruences of algebraic automorphic forms and supercuspidal\n representations
• Potential level-lowering for GSp(4)
• Computing Congruences of Modular Forms and Galois Representations Modulo\n Prime Powers
• Congruences between modular forms modulo prime powers