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We study the rational torsion subgroup of the modular Jacobian $J_0(N)$ for$N$ a square-free integer. We give a new proof of a result of Ohta on ageneralization of Ogg's conjecture: for a prime number $p \nmid 6N$, the$p$-primary part of the rational torsion subgroup equals that of the cuspidalsubgroup. Whereas previous proofs of this result used explicit computations ofthe cardinalities of these groups, we instead use their structure as modulesfor the Hecke algebra.

Another look at rational torsion of modular Jacobians