  For each positive integer k, we investigate the L-function attached to the
k-th symmetric power of the F-crystal associated to the family of cubic
exponential sums of x^3 + \lambda x. We explore its rationality, field of
definition, degree, trivial factors, functional equation, and Newton polygon.
The paper is essentially self-contained, due to the remarkable and attractive
nature of Dwork's p-adic theory.
  A novel feature of this paper is an extension of Dwork's effective
decomposition theory when k < p. This allows for explicit computations in the
associated p-adic cohomology. In particular, the action of Frobenius on the
(primitive) cohomology spaces may be explicitly studied.
