 Theta functions and real analytic Eisenstein series, important in algebraic geometry and number theory, also admit such realizations.A powerful approach to the theory of classical modular forms, initiated by Gelfand, Graev, and Piatetski-Shapiro, views them as matrix coefficients of certain infinite-dimensional unitary representations, automorphic representations of adelic groups.This approach was further developed by Langlands, for general reductive algebraic groups over global fields.