  In this note we prove Sarnak's (spherical) density hypothesis for the full
discrete spectrum of the quotients $\Gamma_{\textrm{pa}}(q)\backslash
\textrm{Sp}_4(\mathbb{R})$, where $\Gamma_{\textrm{pa}}(q)$ are paramodular
groups with square-free level $q$. To derive this estimate we upgrade a density
estimate established via the (pre)-Kuznetsov formula, which only accounts for
the generic part, using Arthur's parametrization of the discrete spectrum.
