  By extending the new supersymmetric localization principle introduced in
\cite{Choi:2021yuz}, we present a path integral derivation of the Selberg trace
formula on arbitrary compact Riemann surfaces, including the case of arbitrary
vector-valued automorphic form and weight corresponding to Maass Laplacian. We
also generalize the method to formulate the Selberg trace formula on generic
compact locally symmetric space.
