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We obtain a Weyl law with power savings for the universal families ofcuspidal automorphic representations, ordered by analytic conductor, of$\mathrm{GL}_2$ over $\mathbb{Q}$, as well as for Hecke characters over anynumber field. The method proceeds by establishing the requisite analyticproperties of the underlying conductor zeta function.

Conductor zeta function for the GL(2) universal family