Explicit parameterizations of ordinary and supersingular regions of

Abstract. In this paper, we explore the geometry of the modular curves X0(p n), over Cp in a few nontrivial examples. In particular, we give explicit rigid-analytic parameterizations of the ordinary and supersingular regions. This is done by first building towers of models for X0(p i), 0 ≤ i ≤ n, and then pulling back the ordinary and supersingular regions of X(1) via the forgetful maps. 1