Abstract
Let ζ be a primitive fifth root of unity and let F be the cyclotomic field F = Q ( ζ ) . Let O ⊂ F be the ring of integers. We compute the Voronoï polyhedron of binary Hermitian forms over F and classify GL 2 ( O ) -conjugacy classes of perfect forms. The combinatorial data of this polyhedron can be used to compute the cohomology of the arithmetic group GL 2 ( O ) and Hecke eigenforms.
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