Explicit modularity of K3 surfaces with complex multiplication of large degree

We consider the transcendental motive of three K3 surfaces $X$ conjectured to have complex multiplication (CM). Under this assumption, we match these to explicit algebraic Hecke quasi-characters $\psi_X$, and CM abelian threefolds $A$. This provides substantial evidence that a power of $A$ corresponds to $X$ under the Kuga-Satake correspondence.