  In this paper, we first investigate the relationship between the number of
primitive representations of $n$ by quadratic forms and the number of
non-primitive ones. We hence obtain a theorem to deal with the Eisenstein
series part with quadratic Dirichlet character when deriving the formula for
the number of primitive representations of an integer $n$ by even rank
quadratic forms from the number of non primitive ones. Formulas for special
cases are given as examples.
