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Computing Hilbert Modular Forms over Fields with Nontrivial Class Group

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Algorithmic Number Theory (ANTS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5011))

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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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Author information

Authors and Affiliations

  1. Institut für Experimentelle Mathematik, Ellernstrasse 29, 45326, Essen, Germany

    Lassina Dembélé

  2. School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Sydney, Australia

    Steve Donnelly

Authors
  1. Lassina Dembélé
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  2. Steve Donnelly
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Editor information

Alfred J. van der Poorten Andreas Stein

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Dembélé, L., Donnelly, S. (2008). Computing Hilbert Modular Forms over Fields with Nontrivial Class Group. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_25

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  • DOI: https://doi.org/10.1007/978-3-540-79456-1_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79455-4

  • Online ISBN: 978-3-540-79456-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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