Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number

  • John Voight
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke eigenvalues associated to Hilbert modular forms of arbitrary level over a totally real field of odd degree. We conclude with two examples which illustrate the effectiveness of our algorithms.


Modular Form Class Number Automorphic Form Quaternion Algebra Real Place 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • John Voight
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of VermontBurlingtonUSA

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