  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
$\mathfrak{su}(3)$-representations of dimension $n$. This is a natural
companion result to work of Romik, who proved an asymptotic formula for the
number of unrestricted $\mathfrak{su}(3)$-representations of dimension $n$.
