Modularity of the Consani-Scholten quintic

Abstract

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over QQ, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livne method to induced four-dimensional Galois representations over QQ. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by Jose Burgos Gil and the second author.Comment: 35 pages, one figure; with an appendix by Jose Burgos Gil and Ariel Pacetti; v3: corrections and improvements thanks to the refere