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