Higher-genus quasimodularity for d-elliptic loci

For $g=2,3$, let $\pi_{g/1,d}$ denote the morphism associated with degree-$d$ covers of genus-$g$ curves to genus-$1$ curves, and let $[(\pi_{g/1,d})_{*}(1)]$ be the resulting Chow class on $\overline{\mathcal{M}}_g$. Writing $\operatorname{Qmod}$ for the ring of quasimodular forms, the proven statement is

$$\sum_{d\ge1}[(\pi_{g/1,d})_{*}(1)]q^d\in A^{g-1}(\overline{\mathcal{M}}_g)\otimes\operatorname{Qmod}.$$

Higher-genus quasimodularity conjecture. The statement of this theorem holds for all $g\ge2$.

The conjecture extends the paper's explicit genus-$2$ and genus-$3$ formulas and asserts quasimodularity of the corresponding Chow-valued generating series in every genus at least $2$.