  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 $T^{{\mathbb D}^r_k}M$, where ${\mathbb D}^r_k$ is the Weil
algebra of $r$-jets at 0 of smooth functions ${\mathbb
R}^k\longrightarrow{\mathbb R}$, for all non-negative integers $n$, $p$, $q$,
$r$, $k$ except the case $p=n$ and $q=0$.
