  Let z be a primitive fifth root of unity and let F be the cyclotomic field
F=Q(z). Let O be the ring of integers. We compute the Voronoi 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 eigen forms.

Number Theory