  A general conjecture of Harder relates the denominator of the Eisenstein
cohomology of certain locally symmetric spaces to special values of
$L$-functions. In this paper we consider the locally symmetric space
$\operatorname{SL}_2(\mathcal{O}) \backslash \mathbb{H}_3$ where $\mathcal{O}$
is the ring of integers of an imaginary quadratic field $K$ and $\mathbb{H}_3$
is the hyperbolic $3$-space. Tobias Berger proves a lower bound on the
denominator of the Eisenstein cohomology in certain cases. The goal of this
paper is to show how results of Ito and Sczech can be used to prove an upper
bound on the denominator in terms of a special value of a Hecke $L$-function.
When the class number of $K$ is one, we combine this result with Berger's
result to obtain the exact denominator.
