In a first course in modular forms, the Eisenstein series of weight 2k are often introduced:
$E_{2k}(z)= \Sigma_{(c,d)=1} 1/2 (cz+d)^{-2k}$.
There is a general definition of Eisenstein series defined in terms of representations induced from Levi subgroups (given, for instance, in some of Arthur's papers on the trace formula). How are these definitions related?