Constructing Hilbert modular forms without exceptional primes
In this paper we construct families of Hilbert modular newforms without exceptional primes. This is achieved by generalizing the notion of good-dihedral primes, introduced by Khare and Wintenberger in their proof of Serre’s modularity conjecture, to totally real fields.
KeywordsGalois representations Hilbert modular forms Level raising theorem Inertial types
Mathematics Subject Classification11F80 11F41
This paper is part of the second author’s Ph.D. thesis. Part of this work has been written during a stay at the Hausdorff Research Institute for Mathematics and a stay, of the second author, at the Mathematical Institute of the University of Barcelona. The authors would like to thank these institutions for their support and the optimal working conditions. The research of L.V.D. was supported by an ICREA Academia Research Prize and by MICINN grant MTM2012-33830. The research of A.Z. was supported by the CONACYT Grant No. 432521/286915.
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