be its Jacobian. For each integer $n \geq 1$, let $T_n$ denote the standard Hecke correspondence on $X_0(N)$; when $p \mid N$, the notation $T_p$ includes the usual degeneracy correspondence customarily denoted $U_p$. Then each $T_n$ induces an endomorphism of abelian varieties over $\mathbb{Q}$,