Hecke realization conjecture for motives of cusp forms

Let $M^n_{\mathrm{cusp}}=M(\overline{\mathcal{M}}_{1,n})_{\varepsilon}[n]$ be the motive associated to the space of cusp forms for $\Gamma=\operatorname{SL}_2(\mathbb{Z})$ of weight $n+1$, with realization $H^1_{\mathrm{cusp}}(\mathcal{Y}_{\Gamma};\mathcal{V}_{n-1})$. Let $T$ be a Hecke correspondence. Hecke realization conjecture. If $T$ vanishes on the space of weight $n+1$ cusp forms, then it vanishes on $M^n_{\mathrm{cusp}}$. This is identified in the source as the remaining conjectural input needed to promote the motivic construction to a complete geometric proof of the Gross–Zagier conjecture; the source does not give a resolution.