2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216843Let 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.11 pages, 1 tableNumber Theory11H55;53C35text