Published online by Cambridge University Press: 01 February 2010
In this paper, the components in the stable model of X0(125) over C5 are determined by constructing (in the language of R. Coleman's ‘Stable maps of curves’, to appear in the Kato Volume of Doc. Math.) an explicit semi-stable covering. Empirical data is then offered regarding the placement of certain CM j-invariants in the supersingular disk of X(1) over C5, which suggests a moduli-theoretic interpretation for the components of the stable model. The paper then concludes with a conjecture regarding the stable model of X0(p3) for p > 3, which is as yet unknown.