Explicit surjectivity of Galois representations attached to abelian surfaces and ${\mathrm{GL}}_2$-varieties

Let $A$ be an absolutely simple abelian variety without (potential) complex multiplication, defined over the number field $K$. Suppose that either $\dim A=2$or$A$isof$\operatorname{GL}_2$-type:wegiveanexplicitbound$\ell_0(A,K)$suchthat,foreveryprime$\ell>\ell_0(A,K)$, the image of the absolute Galois group of $K$ in $\mathrm{Aut}(T_{\mathrm{\ell }}(A))$ is as large as it is allowed to be by endomorphisms and polarizations.