The equivariant Milnor-Witt motive of ${\bar{\mathcal{M}}}_{1,2}$

We provide a decomposition of the equivariant Milnor-Witt motive for the moduli space of stable curves ${\bar{\mathcal{M}}}_{1,2}$. As a result, the equivariant Chow-Witt ring ${\widetilde{CH}}^{\ast }({\bar{\mathcal{M}}}_{1,2})$ is fully determined.