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

### Summary

Summary: 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.

### Mathematics Subject Classification

11F41, 11F80, 11G40, 14G10, 14J32

### Keywords/Phrases

consani-scholten quintic, Hilbert modular form, faltings--Serre--livné method, Sturm bound