We first define spaces of half-integral weight modular forms of
general *p*-adic weight equipped with a Hecke action,
generalizing earlier work in which the weight was required to be
classical. We then define Banach modules of families of
half-integral weight modular forms equipped with a Hecke action.
In both cases the Hecke operators are proven to be continuous
and *U _{p2}* is proven to be compact in the overconvergent case.
These Banach modules are then used to constuct an eigencurve
parameterizing systems of eigenvalues of the Hecke operators acting
on the spaces of half-integral weight modular forms. Along the way
a Coleman-style theorem indicating that eigenforms of low slope are
classical is proven.