  The aim of this article is to show that p-adic geometry of modular curves is
useful in the study of p-adic properties of traces of singular moduli. In order
to do so, we partly answer a question by Ono. As our goal is just to illustrate
how p-adic geometry can be used in this context, we focus on a relatively
simple case, in the hope that others will try to obtain the strongest and most
general results. For example, for p=2, a result stronger than Thm.1 is proved
in [Boylan], and a result on some modular curves of genus zero can be found in
[Osburn] . It should be easy to apply our method, because of its local nature,
to modular curves of arbitrary level, as well as to Shimura curves.
