Modularity of the Consani-Scholten Quintic With an Appendix by José Burgos Gil and Ariel Pacetti

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over $\Q$, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livné method to induced four-dimensional Galois representations over $\Q$. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author.

2010 Mathematics Subject Classification: Primary: 11F41; Secondary: 11F80, 11G40, 14G10, 14J32

Keywords and Phrases: Consani-Scholten quintic, Hilbert modular form, Faltings--Serre--Livné method, Sturm bound

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