  Let p>2 be a prime and let X be a compactified PEL Shimura variety of type
(A) or (C) such that p is an unramified prime for the PEL datum. Using the
geometric approach of Andreatta, Iovita, Pilloni, and Stevens we define the
notion of families of overconvergent locally analytic p-adic modular forms of
Iwahoric level for X. We show that the system of eigenvalues of any finite
slope cuspidal eigenform of Iwahoric level can be deformed to a family of
systems of eigenvalues living over an open subset of the weight space. To prove
these results, we actually construct eigenvarieties of the expected dimension
that parametrize systems of eigenvalues appearing in the space of families of
cuspidal forms.
