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arXiv · 1703.05200

The sporadic group J2, Hauptmodul and Belyi map

Hartmut Monien
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Abstract

Determining Fourier coefficients of modular forms of a finite index noncongruence subgroups of the modular group is still a non-trivial task. In this brief note we describe a new algorithm to reliably calculate an approximation for a modular form of a given weight. As an example we calculate the hauptmodul and Belyi map of a genus zero subgroup of the modular group defined via a canonical homomorphism by the second Janko group. Our main result is the field of definition of its Belyi map, the explicit Belyi map and the Fourier coefficients of its hauptmodul.

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Hartmut Monien. 2017-03-15. The sporadic group J2, Hauptmodul and Belyi map. https://arxiv.org/abs/1703.05200

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