On Ribet's level-raising theorem for U (3)

Abstract

A well-known theorem of Ken Ribet asserts that, under certain assumptions, a modular form (mod ℓ) on Γ 0 ( N ) can be "lifted" to yield a newform on Γ 0 ( N ℓ) with the same modular Galois representation. For further progress in the modular theory of automorphic forms one will need to understand this phenomenon for automorphic forms on reductive groups other than GL(2). In this paper we prove such a result for the unitary group of rank 3, under suitable assumptions. The proof relies on the modular representation theory of p -adic reductive groups.