Computing Hilbert modular forms over fields with nontrivial class group

Details Computing Hilbert modular forms over fields with nontrivial class group Computing Hilbert modular forms over fields with nontrivial class group

2007-11-26

arxiv.org/abs/0711.3863v1

Mathematics

Number Theory

Scientific paper

In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over $\Q(\sqrt{10})$ and $\Q(\sqrt{85})$ and their Hilbert class fields, we present some new instances of the conjectural Eichler-Shimura construction for totally real fields, and in particular find new examples of modular abelian varieties with everywhere good reduction.

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