  In this paper we determine the components in the stable model of X_0(125)
over C_5 by constructing in rigid-analytic terminology an explicit semi-stable
covering. We then offer empirical data regarding the placement of certain CM
j-invariants in the supersingular disk of X(1)/C_5 which suggests a
moduli-theoretic interpretation of the components in the stable model. The
paper then concludes with a conjecture regarding the stable model of X_0(p^3)
for p>3, which is as yet unknown.
