On the faithfulness of parabolic cohomology as a Hecke module over a finite field

Abstract

This article exhibits conditions under which a certain parabolic group cohomology space over a finite field F is a faithful module for the Hecke algebra of cuspidal Katz modular forms over an algebraic closure of F. These results can e.g. be applied to compute cuspidal Katz modular forms of weight one with methods of linear algebra over F.