Chung--Moon's Euler characteristic conjecture for line bundles on moduli spaces

Let $M_{d,\chi}$ be the moduli space of one-dimensional sheaves on $\mathbb{P}^2$ with degree $d$ and Euler characteristic $\chi$, let $c_0(2)$ denote the normalized tautological class used in the paper, and let $\chi(M_{d,\chi},m\cdot c_0(2))$ denote the Euler characteristic of the corresponding line bundle. Chung--Moon's conjecture. For $d\geq 1$ and coprime $\chi$, we have

$$\chi\big(M_{d, \chi},\, m\cdot c_0(2)\big) = \binom{m+3d-1}{m}.$$

This predicts a closed formula for Euler characteristics of these tautological line bundles uniformly in $d$, $m$, and coprime $\chi$. The supplied text identifies it as a conjecture of Chung--Moon but gives no resolution evidence.