Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti

Abstract

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over $\mathbb{Q}$, 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 $\mathbb{Q}$. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author.