  Let $F$ be a non-Archimedean local field with the ring of integers
$\mathcal{O}$ and the prime ideal $\mathfrak{p}$ and let $G={\bf
G}\left(\mathcal{O}/\mathfrak{p}^n\right)$ be the adjoint Chevalley group. Let
$m_f(G)$ denote the smallest possible dimension of a faithful representation of
$G$. Using the Stone-von Neumann theorem, we determine a lower bound for
$m_f(G)$ which is asymptotically the same as the results of Landazuri, Seitz
and Zalesskii for split Chevalley groups over $\mathbb{F}_q$. Our result yields
a conceptual explanation of the exponents that appear in the aforementioned
results
