For every N and every prime l, the l-primary subgroup of the rational cuspidal divisor class group of X_0(N) is a direct sum of explicit cyclic subgroups generated by the new divisors Z_l(d).
More precisely, we pr ove the following, which is a combination of Theorems 1.5 and 1.6
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The rational cuspidal divisor class group of $X_0(N)$
For every N and every prime l, the l-primary subgroup of the rational cuspidal divisor class group of X_0(N) is a direct sum of explicit cyclic subgroups generated by the new divisors Z_l(d).