l-Adic representations associated to modular forms over imaginary quadratic fields

Tobias Berger, Gergely Harcos

Published 2007-07-09Version 1

Let pi be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K such that the central character of pi is invariant under the non-trivial automorphism of K. We show that pi is associated with an l-adic Galois representation rho over K such that at each prime of K outside an explicit finite set the Frobenius polynomial of rho agrees with the Hecke polynomial of pi.