Modularity of a certain "rank-2 attractor" Calabi-Yau threefold

We attempt to prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was essentially conjectured by Meyer and Verrill. It was revisited in its present form by Candelas, de la Ossa, Elmi and van Straten, whose computations of Euler factors in a whole pencil of Calabi-Yau threefolds highlighted this fibre as one of three overwhelmingly likely to be ``rank-2 attractors''. Unfortunately there is an error in Section 7.