Meromorphic-power conjecture for Selberg zeta-functions in the index-six cusp case

Let $\Gamma$ be a cofinite Kleinian group with finite-dimensional unitary representation $\chi$, and let $\Gamma_\infty$ and $\Gamma'_\infty$ denote the cusp stabilizer and its translation subgroup, respectively. Suppose that

$$[\Gamma_\infty:\Gamma'_\infty]=6.$$

Meromorphic-power conjecture. Then there is an integer $N$ such that

$$Z(s,\Gamma,\chi)^N$$

is a meromorphic function.

This conjecture concerns the remaining cusp-index case in the analysis of the Selberg trace formula. The preceding index-four case is proved to have the analogous property, but the source gives no resolution for the index-six case.