Sums of class numbers and mixed mock modular forms

In this paper, we consider sums of class numbers of the type $\sum_{m\equiv a\pmod{p}} H(4n-m^2)$,where$p$isanoddprime,$n\in $\mathbb{N}$,$and$a\in $\mathbb{Z}$$. By showing that these are coefficients of mixed mock modular forms, we obtain explicit formulas. Using these formulas for $p=5$ and $7$, we then prove a conjecture of Brown et al. in the case that $n=\mathrm{\ell }$ is prime.