The stable reduction of X(p^2)

I will report on partial results on the problem of computing the stable
reduction of modular curves of level p^n, for n>1. This is joint work with
Irene Bouw. So far we have completely determined the stable reduction of
X(p^2). Form this one can deduce the stable reduction of X_0(p^3) and
X_0(p^4), which goes beyond the previously known results, due to
Deligne-Rapoport and Edixhoven.