  We present results of our computation of the topological susceptibility with
$N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the
method of spectral projectors. We perform a detailed study of the quark mass
dependence and discretization effects. We make an attempt to confront our data
with chiral perturbation theory and extract the chiral condensate from the
quark mass dependence of the topological susceptibility. We compare the value
with the results of our direct computation from the slope of the mode number.
We emphasize the role of autocorrelations and the necessity of long Monte Carlo
runs to obtain results with good precision. We also show our results for the
spectral projector computation of the ratio of renormalization constants
$Z_P/Z_S$.
