Torsions in cohomology of [formula omitted] and congruence of modular forms

Abstract

We describe torsion classes in the first cohomology group of SL2(Z). In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology group of SL2(Z) as a module over the torsion invariants. As application, we obtain various congruences between cuspidal forms of level one and torsion Eisenstein classes.