Symmetric powers and modular invariants of elementary abelian p-groups

Let $E$ be a elementary abelian $p$-group of order $q=p^n$. Let $W$ be a faithful indecomposable representation of $E$ with dimension 2 over a field $k$ of characteristic $p$, and let $V= S^m(W)$ with $mmodular invariants of cyclic groups of order $p$. If $mWoodcock for cyclic groups of order $p$. Our methods are primarily representation-theoretic, and along the way we prove that for any $dcyclic groups of prime order.