  We study a generalized Dedekind sum $S_{\chi_1,\chi_2}(a,c)$ attached to
newform Eisenstein series $E_{\chi_1,\chi_2}(z,s)$. Our work shows the Dedekind
sum is rarely substantially larger than $\log^3 c$. The method of proof first
relates the size of the Dedekind sum to continued fractions. A result of
Hensley from 1991 then controls the average size of the maximal partial
quotient in the continued fraction expansion of $a/c$.
  We complement this result by computing approximate values of the Dedekind sum
in some special cases, which in particular produces examples of large values of
the Dedekind sum.
