  Fix a prime number p and choose, once and for all, an embedding of the
algebraic closure of Q into Qp. Let k and N be integers, and suppose N is not
divisible by p. If f is a modular form of weight k, level N, and trivial
character which is an eigenform for the p-th Hecke operator Tp, we define the
slope of f to be the p-adic valuation of the eigenvalue of Tp. This paper
reports on computations that suggest that there is quite a lot of structure to
the set of slopes for eigenforms of varying weight k. In particular, we find
that the slopes are often smaller than expected, that they are almost always
integers, that there is evidence of a connection between fractional slopes and
slopes which are "bigger than usual", and that there are some hints of a
connection to the theory of theta-cycles.
