  We carry out "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 also consider
Eisenstein series of weight $2$ with level, and Eisenstein series with
character.

Number Theory