Semisimple Torsion Fields of Modular Jacobians at Powers of 11 and 13

For ell in {11,13} and every m >= 1, we identify the semisimple ell-torsion field of the Jacobian of the connected principal modular curve X(ell^m) over K_m = Q(zeta_(ell^m)). It is the compositum of K_m with the field cut out by the residual Ramanujan Delta representation, and its Galois group over K_m is SL_2(F_ell). The full torsion field has an ell-group kernel over this quotient; the prime-to-ell part of its degree is exactly 120 or 168, respectively. The result is an explicit structural corollary of level-one modularity, the modular decomposition of Jacobians, and Hoshi-Iijima's non-pro-ell theorem. We give a cyclotomic-field moduli construction of the covering needed in the argument and reproducible exact certificates for the two residual Delta images. We do not determine the full torsion field or claim to resolve the unrestricted AIM splitting-field question. This note is an unrefereed synthesis; absolute priority is not asserted.