Faber–van der Geer conjectural formula for strict endoscopic Euler characteristics

Let $\mathcal{A}_2$ be the moduli space of principally polarized abelian surfaces, let $\mathbb{V}(\lambda)$ be the local system of weight $\lambda=(l,m)$, and let $e_{\mathrm{endo}}(\mathcal{A}_2,\mathbb{V}(\lambda))$ denote the motivic Euler characteristic of the strict endoscopic part of the inner cohomology. For sufficiently regular $\lambda$, this strict endoscopic part is defined from

$$H_{\mathrm{End}^{\mathrm{s}}}^{3}(\mathcal{A}_2,\mathbb{V}(\lambda))=\bigoplus_{\pi\in\mathcal{C}}m(\pi)(\pi_{fin})^{K_0},$$

where $K_0$ is the standard paramodular level subgroup and $\mathcal{C}$ consists of the irreducible cuspidal automorphic representations whose contribution to $H^3_!(\mathcal{A}_2,\mathbb{V}(\lambda))$ vanishes. Faber–van der Geer's conjecture. With this notation, for sufficiently regular $\lambda=(l,m)$,

$$e_{\mathrm{endo}}(\mathcal{A}_2,\mathbb{V}(\lambda))=-s_{l+m+4}S[l-m+2]\mathbb{L}^{m+1}.$$

The formula gives a motivic description of the strict endoscopic contribution to the cohomology of the genus-two Siegel modular variety. The supplied text attributes it to C. Faber and G. van der Geer but does not state whether it has been proved or disproved.