Density-Ramanujan conjecture for congruence complexes

Let $G$ be a definite Gross inner form and let $\mathfrak{p}$ be a finite place. Let $\{X_{\mathfrak{p}}(q)\}$ denote its family of congruence complexes. Density-Ramanujan conjecture. For any definite Gross inner form $G$ and any finite place $\mathfrak{p}$, the family $\{X_{\mathfrak{p}}(q)\}$ forms a family of density-Ramanujan complexes. The source states this as a conjecture about congruence complexes; no resolution is given.