Computing Hilbert Modular Forms over Fields with Nontrivial Class Group

  • Lassina Dembélé
  • Steve Donnelly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5011)

Abstract

We exhibit an algorithm for the computation of Hilbert modular forms over an arbitrary totally real number field of even degree, extending results of the first author. We present some new instances of the conjectural Eichler-Shimura construction for totally real number fields over the fields \({\mathbb{Q}}(\sqrt{10})\) and \({\mathbb{Q}}(\sqrt{85})\) and their Hilbert class fields, and in particular some new examples of modular abelian varieties with everywhere good reduction over those fields.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lassina Dembélé
    • 1
  • Steve Donnelly
    • 2
  1. 1.Institut für Experimentelle MathematikEssenGermany
  2. 2.School of Mathematics and Statistics F07University of SydneySydneyAustralia

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