Modular units and cuspidal divisor classes on X0(n2M) with n|24 and M squarefree.

For a positive integer N , let C (N) be the subgroup of J 0 (N) generated by the equivalence classes of cuspidal divisors of degree 0 and C (N) (Q) : = C (N) ∩ J 0 (N) (Q) be its Q -rational subgroup. Let also C Q (N) be the subgroup of C (N) (Q) generated by Q -rational cuspidal divisors. We prove that when N = n 2 M for some integer n dividing 24 and some squarefree integer M , the two groups C (N) (Q) and C Q (N) are equal. To achieve this, we show that all modular units on X 0 (N) on such N are products of functions of the form η (m τ + k / h) , m h 2 | N and k ∈ Z and determine the necessary and sufficient conditions for products of such functions to be modular units on X 0 (N). [ABSTRACT FROM AUTHOR]