Structure of the cuspidal rational torsion subgroup of J(1)(p(n))

Abstract

Let p be a prime and let J(1)(p(n)) denote the Jacobian of the modular curve X(1)(p(n)). The Jacobian J(1)(p(n)) contains a Q-rational torsion subgroup generated by the cuspidal divisor classes [(a/p(n))-(infinity)], where p inverted iota a. In this paper, we determine the structure of the p-primary subgroup of this Q-rational torsion subgroup in the case where p is a regular prime.