#### Document Type

Article

#### Version

Publisher's PDF

#### Publication Title

Mathematics of Computation

#### Volume

75

#### Publication Date

2006

#### Abstract

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results.

#### Publisher's Statement

First published in *Mathematics of Computation* in 2006, published by the American Mathematical Society.

#### Citation

Grundman, H.G., and L.E. Lippincott. "Computing the Arithmetic Genus of Hilbert Modular Fourfolds." *Math. Comp.* 75 (2006): 1553-1560.

#### DOI

10.1090/S0025-5718-06-01842-4