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

John Voight

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arXiv · 1004.5340

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

John Voight

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Abstract

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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John Voight. 2010-04-29. Computing automorphic forms on Shimura curves over fields with arbitrary class number. https://arxiv.org/abs/1004.5340

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