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 $p\geq 5$.
@article{10_4064_ap90_1_7,
author = {Grzegorz Kapustka and Micha{\l} Kapustka},
title = {Modularity of a nonrigid {Calabi{\textendash}Yau} manifold
with bad reduction at 13},
journal = {Annales Polonici Mathematici},
pages = {89--98},
year = {2007},
volume = {90},
number = {1},
doi = {10.4064/ap90-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap90-1-7/}
}
TY - JOUR
AU - Grzegorz Kapustka
AU - Michał Kapustka
TI - Modularity of a nonrigid Calabi–Yau manifold
with bad reduction at 13
JO - Annales Polonici Mathematici
PY - 2007
SP - 89
EP - 98
VL - 90
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%A Michał Kapustka
%T Modularity of a nonrigid Calabi–Yau manifold
with bad reduction at 13
%J Annales Polonici Mathematici
%D 2007
%P 89-98
%V 90
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap90-1-7/
%R 10.4064/ap90-1-7
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Grzegorz Kapustka; Michał Kapustka. Modularity of a nonrigid Calabi–Yau manifold
with bad reduction at 13. Annales Polonici Mathematici, Tome 90 (2007) no. 1, pp. 89-98. doi: 10.4064/ap90-1-7
