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Computing Hilbert modular forms for fields with nontrivial class group

Lassina Dembélé and Steve Donnelly

Number 16
Author Lassina Dembélé
Project A09
Year 2008

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(10−−√) and Q(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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