  In this paper, we study the moduli space of unipotent Weil-Deligne
representations and characterise which irreducible components are smooth. We
also study a certain class of unions of irreducible components, and prove that
they are Cohen-Macaulay at points $(\Phi, N)$ with $\Phi$ regular semisimple.
We apply the smoothness results proved earlier to show that a certain space of
ordinary automorphic forms is a locally generically free module over the
corresponding global deformation ring.
