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Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. Is it known whether the space $$ \mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ is finite dimensional for $\pi\in\widehat G$? This is true if $\Gamma$ is cocompact, but in general?

Here Hom$_G$ refers to $G$-equivariant, continuous linear maps.

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. Is it known whether the space $$ \mathrm{Hom}_G\left(\pi,L^2(\Gamma\backslash G)\right) $$ is finite dimensional for $\pi\in\widehat G$? This is true if $\Gamma$ is cocompact, but in general?

Here Hom$_G$ refers to $G$-equivariant, continuous linear maps.

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. Is it known whether the space $$ \mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ is finite dimensional for $\pi\in\widehat G$? This is true if $\Gamma$ is cocompact, but in general?

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. Is it known whether the space $$ \mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ is finite dimensional for $\pi\in\widehat G$? This is true if $\Gamma$ is cocompact, but in general?

Here Hom$_G$ refers to $G$-equivariant, continuous linear maps.