Let $J_1(p)$ be the Jacobian of the modular curve $X_1(p)$ for p an odd prime. We know that $J_1(p)$ is isogenous to a direct sum of abelian varieties $\oplus_{f}A_f$ where the sum runs over Hecke/eigen cusp forms of weight two which are not Galois conjugates of each other. When are the abelian varieties $A_f$ Jacobians? Any comments/references will be much appreciated.



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