  Let $G$ be a Lie-group and $\Ga\subset G$ a cocompact lattice. For a
finite-dimensional, not necessarily unitary representation $\om$ of $\Ga$ we
show that the $G$-representation on $L^2(\Ga\bs G,\om)$ admits a complete
filtration with irreducible quotients. As a consequence, we show the trace
formula for non-unitary twists and arbitrary locally compact groups.
