Perfect forms, K-theory and the cohomology of modular groups

For N=5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoï cell complexes attached to the modular groups SLN(Z) and GLN(Z). From this we deduce the rational cohomology of those groups and some information about Km(Z), when m=5,6 and 7.