Linear natural liftings of forms to Weil bundles with Weil algebras D-k(r)

We give an explicit description and calculate the dimension of the vector space of linear natural liftings of p-forms on n-dimensional manifolds M to q-forms on T(sic) M, where D-k(r) is the Weil algebra of r-jets at 0 of smooth functions R-k -> R, for all non-negative integers n, p, q, r, k except the case p = n and q = 0.