The point-count and Calabi-Yau resolution conjecture for V_{32}/G_4

Let $V_{32}$ be the double cover considered in the paper, and let $G_4=\langle\alpha_1,\alpha_2\rangle$. Write $[V_{32}/G_4]_p$ for the number of points of the quotient over $\mathbb F_p$, and let $a_{6,p}$ be the relevant Hecke eigenvalue in weight $6$. A strongly rigid Calabi–Yau resolution is a strongly rigid resolution of singularities that is Calabi–Yau. Point-count and resolution conjecture for $V_{32}/G_4$. For every prime $p>2$,

$$[V_{32}/G_4]_p=\sum_{i=0}^5p^i-a_{6,p},$$

and $V_{32}/G_4$ has a strongly rigid Calabi–Yau resolution. The point-count formula is suggested by computations for $p<20$, while the existence of the asserted resolution remains unproved in the supplied context.