The homology of SL2(Z[1/m])SL2(Z[1/m]) for small m

We describe an algorithm for computing finitely many terms of a free ZGZG-resolution of ZZ for G   a finite index subgroup of SL2(Z[1/m])SL2(Z[1/m]). An implementation of the algorithm is used to determine the integral homology groups Hn(SL2(Z[1/m]),Z)Hn(SL2(Z[1/m]),Z) for all integers m⩽50m⩽50, m≠30,42m≠30,42 and n⩾0n⩾0. For m=30m=30 or m=42m=42 the implementation is practical only for n=1,2n=1,2.