  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.
