manuscripta mathematica

, 125:1

Companion forms over totally real fields


DOI: 10.1007/s00229-007-0128-9

Cite this article as:
Gee, T. manuscripta math. (2008) 125: 1. doi:10.1007/s00229-007-0128-9


We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2 < k < p, which is ordinary at all primes dividing p and has tamely ramified Galois representation at all primes dividing p, then there is a “companion form” of parallel weight k′ := p + 1 − k. This work generalises results of Gross and Coleman–Voloch for modular forms over Q.

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK