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Modularity of a nonrigid Calabi-Yau manifold with bad reduction at 13

Grzegorz Kapustka, Michał Kapustka (2007)

Annales Polonici Mathematici

We identify the weight four newform of a modular Calabi-Yau manifold studied by Hulek and Verrill. The main obstacle is that this Calabi-Yau manifold is not rigid and has bad reduction at prime 13. Replacing the original fiber product of elliptic fibrations with a fiberwise Kummer construction we reduce the problem to studying the modularity of a rigid Calabi-Yau manifold with good reduction at primes p ≥ 5.

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