  We study the 'spectral projector' method for the computation of the chiral
condensate and the topological susceptibility, using $N_f=2+1+1$ dynamical
flavors of maximally twisted mass Wilson fermions. In particular, we perform a
study of the quark mass dependence of the chiral condensate $\Sigma$ and
topological susceptibility $\chi_{top}$ in the range $270 MeV < m_{\pi} < 500
MeV$ and compare our data with analytical predictions. In addition, we compute
$\chi_{top}$ in the quenched approximation where we match the lattice spacing
to the $N_f=2+1+1$ dynamical simulations. Using the Kaon, $\eta$ and
$\eta^{\prime}$ meson masses computed on the $N_f=2+1+1$ ensembles, we then
perform a preliminary test of the Witten-Veneziano relation.
