  We demonstrate that the 3-power torsion points of the Jacobians of the
principal modular curves X(3^n) are fixed by the kernel of the canonical outer
Galois representation of the pro-3 fundamental group of the projective line
minus three points. The proof proceeds by demonstrating the curves in question
satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the
second part of the criterion are provided; the first relies on a theorem of
Shimura, while the second uses the moduli interpretation.
