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Let $\\ell$ be a prime and let $\\bar{\\rho}_{A,\\ell} : G_{\\mathbb{Q}} \\rightarrow \\mathrm{GSp}_{2d}(\\mathbb{F}_\\ell)$ be the representation giving the action of $G_{\\mathrm{Q}} :=\\mathrm{Gal}(\\bar{\\mathrm{Q}}/\\mathrm{Q})$ on the $\\ell$-torsion group $A[\\ell]$. 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