On the number of irreducible representations of $\mathfrak{s}\mathfrak{u}(3)$

In this note, we use a variant of the hyperbola method to prove an asymptotic expansion for the summatory function of the number of irreducible $\mathfrak{s}\mathfrak{u}(3)$-representations of dimension $n$. This is a natural companion result to work of Romik, who proved an asymptotic formula for the number of unrestricted $\mathfrak{s}\mathfrak{u}(3)$-representations of dimension $n$.