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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(mτ + k/h), mh 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).

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