Motivic Galois representations valued in Spin groups

Let $m$ be an integer such that $m\ge 7$ and $m\equiv 0,1,7\mathrm{m}\mathrm{o}\mathrm{d}8$. We construct strictly compatible systems of representations of $\Gamma_{\mathbb Q} \to $\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}$_m(\overline{\mathbb Q}_l) \xrightarrow{$\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}$} $\mathrm{G}\mathrm{L}$_N(\overline{\mathbb Q}_l)$ that is potentially automorphic and motivic. As an application, we prove instances of the inverse Galois problem for the ${\mathbb{F}}_p$–points of the spin groups. For odd $m$, we compare our examples with the work of A. Kret and S. W. Shin, which studies automorphic Galois representations valued in ${\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}}_m$.