A modular quintic Calabi-Yau threefold of level 55

TL;DR

This paper identifies a specific modular Calabi-Yau threefold of level 55 within the Horrocks-Mumford family, linking its cohomology to a classical modular form, advancing understanding of Calabi-Yau modularity.

Contribution

It locates a new modular Calabi-Yau threefold of level 55 in the parameter space of Horrocks-Mumford quintics, establishing a connection to a classical modular form.

Findings

The threefold's L-function matches a modular form of weight 4 and level 55.

The paper demonstrates the existence of modularity in this specific Calabi-Yau threefold.

It expands the catalog of known modular Calabi-Yau varieties.

Abstract

In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight 4 and level 55.