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Let $G$ be a reductive algebraic group over $\mathbb{Q}$ and $\Gamma\subsetG(\mathbb{Q})$ an arithmetic subgroup. Let $K_\infty\subset G(\mathbb{R})$ be amaximal compact subgroup. We study the asymptotic behavior of the countingfunctions of the cuspidal and residual spectrum, respectively, of the regularrepresentation of $G(\mathbb{R})$ in $L^2(\Gamma\backslash G(\mathbb{R}))$ of afixed $K_\infty$-type $\sigma$. A conjecture, which is due to Sarnak, statesthat the counting function of the cuspidal spectrum of type $\sigma$ satisfiesWeyl's law and the residual spectrum is of lower order growth. Using the Arthurtrace formula we reduce the conjecture to a problem about $L$-functionsoccurring in the constant terms of Eisenstein series. If $G$ satisfies property(L), introduced by Finis and Lapid, we establish the conjecture. This includesclassical groups over a number field.

The Weyl law for congruence subgroups and arbitrary $K_\infty$-types