Explicit surjectivity of Galois representations for abelian surfaces and GL2-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 is of GL2-type: we give an explicit bound ℓ0(A,K) such that, for every prime ℓ>ℓ0(A,K), the image of Gal(K‾/K) in Aut(Tℓ(A)) is as large as it is allowed to be by endomorphisms and polarizations.