  We give asymptotics for shifted convolutions of the form $$\sum_{n < X}
\frac{\sigma_{2u}(n,\chi)\sigma_{2v}(n+k,\psi)}{n^{u+v}}$$ for nonzero complex
numbers $u,v$ and nontrivial Dirichlet characters $\chi,\psi$. We use the
technique of "automorphic regularization" to find the spectral decomposition of
a combination of Eisenstein series which is not obviously square-integrable.
The error term we obtain is in some cases smaller than what the method we use
typically yields.
