Computing the Level of a Modular Rigid Calabi-Yau Threefold

Abstract

In a previous article (see Dieulefait and Manoharmayum), the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and reprove) a result of Serre giving a bound for the conductor of "integral" two-dimensional compatible families of Galois representations and apply this result to give an algorithm that determines the level of a modular rigid Calabi-Yau threefold. We apply the algorithm to three examples.