Ramanujan conjecture for SU(3) bigraphs

Let $G$ be the $p$-adic group and $I$ an Iwahori subgroup, and let $\Gamma$ be a cocompact lattice in $G$. Consider the space of $I$-invariant vectors

$$L^2(G/\Gamma)^I=L^2(I\backslash G/\Gamma).$$

An irreducible unitary $\mathcal H(G,I)$-module is called tempered when its character satisfies the temperedness condition $|\operatorname{Tr}_\varphi(\theta)|\leq 2$. Ramanujan conjecture. Every nontrivial irreducible unitary $\mathcal H(G,I)$-module that appears in the decomposition of $L^2(G/\Gamma)^I=L^2(I\backslash G/\Gamma)$ is tempered. This is the representation-theoretic formulation of the Ramanujan condition for the associated SU(3) bigraph; the source provides no resolution, so the conjecture is left open.