We identify the weight four newform of a modular Calabi-Yau manifold studied by Hulek and Verrill. The main obstacle is that this Calabi-Yau manifold is not rigid and has bad reduction at prime 13. Replacing the original fiber product of elliptic fibrations with a fiberwise Kummer construction we reduce the problem to studying the modularity of a rigid Calabi-Yau manifold with good reduction at primes p ≥ 5.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-7,
author = {Grzegorz Kapustka and Micha\l\ Kapustka},
title = {Modularity of a nonrigid Calabi-Yau manifold with bad reduction at 13},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {89-98},
zbl = {1114.14015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-7}
}
Grzegorz Kapustka; Michał Kapustka. Modularity of a nonrigid Calabi-Yau manifold with bad reduction at 13. Annales Polonici Mathematici, Tome 92 (2007) pp. 89-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-1-7/