I'd like to construct a subgroup of Sp(4,Z) of the form:
G0(N)=M(N)∩Sp(4,Z)
where M(N) is a 4×4 matrix over the integer ring with elements that are multiples of the integer N. I think I know how to construct such an M(N) for a given N, but how does one then construct such a subgroup G0(N)? Thanks!