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What is The sporadic group J2, Hauptmodul and Belyi map about?

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.

Author

Monien, Hartmut

Published

2017

Language

EN