Cohomology of congruence subgroups of SL(4,Z) II

In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212] we computed cohomology groups H (Γ0(N),C), where Γ0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N . In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212]. The cuspidal cohomology classes in this paper are the first cuspforms for GL(4) concretely constructed in terms of Betti cohomology. © 2007 Published by Elsevier Inc. MSC: primary 11F75; secondary 11F23, 11F46