The (almost) integral Chow ring of ${\tilde{\mathcal{M}}}_3^7$

This paper is the third in a series of four papers aiming to describe the (almost integral) Chow ring of ${\bar{\mathcal{M}}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we compute the Chow ring of ${\tilde{\mathcal{M}}}_3^7$ with $\mathbb{Z}[1\mathrm{/}6]$-coefficients.