Given a finite subgroup $\Gamma$ of $O(4)$ acting freely on $S^3$, is there any reference for the spectrum of Laplacian for the transverse-traceless symmetric $2$-tensor on $S^3/\Gamma$ equipped with the standard metric?

More precisely, I am interested in computing explicitly the eigenvalue $\lambda \ge 0$ such that $$ \Delta h +\lambda h=0 $$ where $h$ is a symmetric $2$-tensor on $S^3/\Gamma$ such that $\text{tr}_gh=\text{div}_gh=0$.

Notice that if $\Gamma$ is trivial, it follows from the paper "Symmetric Tensor Eigen Spectrum of the Laplacian on n Spheres" that $\lambda=m^2+2m-2$ for $m=2,3,\cdots$.