  We obtain a simple formula for the multiplicity of eigenvalues of the
Hodge-Laplace operator, $\Delta_f$, acting on sections of the full exterior
bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy
group Z_2^k, with 0<k<n. This formula implies that any two compact flat
manifolds with holonomy group Z_2^k having isospectral lattices of translations
are isospectral on forms, that is, with respect to $\Delta_f$. As a
consequence, we construct a large family of pairwise $\Delta_f$-isospectral and
nonhomeomorphic n-manifolds of cardinality greater than $2^{(n-1)(n-2)/2}$.
