  In a previous article (a joint work with J. Manoharmayum) the modularity of a
large class of rigid Calabi-Yau threefolds was established. To make that result
more explicit, we recall (and re-prove) a result of Serre giving a bound for
the conductor of an "integral" 2-dimensional compatible family 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.
