THE SHIMURA SUBGROUP OF J0(N)

To the natural morphism X1(N) --> X0(N) of modular curves corresponds, by Picard functoriality, a morphism J0(N) --> J1(N) between their Jacobian varieties. Its kernel SIGMA(N), called the Shimura subgroup of J0(N), is finite. We determine the group structure of SIGMA(N) together with the action of Galois and the action of the Hecke algebra. This extends previous results obtained by B. Mazur and K. Ribet.