Another look at rational torsion of modular Jacobians

We study the rational torsion subgroup of the modular Jacobian [Formula: see text] for N a square-free integer. We give a proof of a result of Ohta on a generalization of Ogg’s conjecture: For a prime number [Formula: see text] , the p-primary part of the rational torsion subgroup equals that of the cuspidal subgroup. Whereas previous proofs of this result used explicit computations of the cardinalities of these groups, we instead use their structure as modules for the Hecke algebra.