Computing automorphic forms on Shimura curves over fields with arbitrary class number

Details Computing automorphic forms on Shimura curves over fields with arbitrary class number Computing automorphic forms on Shimura curves over fields with arbitrary class number

2010-04-29

arxiv.org/abs/1004.5340v1

Mathematics

Number Theory

15 pages; final submission to ANTS IX

Scientific paper

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.

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