## Abstract

Let F be a totally real field and p ≥ 3 a prime. If ρ : Gal(F̄/F) → GL_{2} (|double strok F sign̄_{p}) is continuous, semisimple, totally odd, and tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which ρ is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which required p to be unramified in F. We also prove a theorem that verifies one half of the conjecture in many cases and use Dembélé's computations of Hilbert modular forms over ℚ(√5 ) to provide evidence in support of the conjecture.

Original language | English |
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Pages (from-to) | 369-391 |

Number of pages | 23 |

Journal | Israel Journal of Mathematics |

Volume | 166 |

DOIs | |

State | Published - Aug 2008 |

Externally published | Yes |

### Bibliographical note

Funding Information:∗ The author thanks the NSF for a Graduate Research Fellowship that supported him during part of this work. Received October 16, 2006 and in revised form February 14, 2007

### Funding

∗ The author thanks the NSF for a Graduate Research Fellowship that supported him during part of this work. Received October 16, 2006 and in revised form February 14, 2007

Funders | Funder number |
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National Science Foundation |