Given an extremal K3 surface $S$ over $\mathbb{Q}$ (i.e. a K3 surface with maximal Picard rank) there is a 2-dimensional Galois representation on the transcendental lattice $T(S)$, and an associated cusp modular form of weight three. This is of course the modularity of extremal K3 surfaces, generalizing the famous result on elliptic curves. See, for example, Theorem 2.2 of (https://arxiv.org/pdf/1212.4308.pdf).

**So are there weight 3 modular forms similarly associated to singular abelian surfaces over $\mathbb{Q}$? Can anyone point me to any literature where these are computed?**

A singular abelian surface is an abelian surface with maximal Picard rank 4, and any such is isogenous to a product of elliptic curves with CM. The transcendental lattice (middle cohomology modulo the algebraic cycles) is then 2-dimensional and should conceivably carry a Galois representation. Which should have an associated modular form. Is this out there in the literature somewhere?