In this talk, we discuss “Hecke summation” for the classical Eisenstein series E_k in an adelic setting. The connection between classical and adelic functions is made by explicit calculations of local and global intertwining operators and Whittaker functions. In the process we determine the automorphic representations generated by the E_k, in particular for k = 2, where the representation is neither a pure tensor nor has finite length. We will also present the analogous results for Eisenstein series of weight 2 with level, and Eisenstein series with character if time permits. This is a joint work with Manami Roy and Ralf Schmidt.