# Number Theory Seminar

Speaker: Hartmut Monien, Univ. Bonn

Title: Belyi maps of non-congruence subgroups of the modular group associated to sporadic groups.

Abstract: Determining Fourier coefficients of modular forms of a finite index noncongruence subgroups of $PSL_2(Z)$ is still a non-trivial task. In my talk I will describe a new algorithm to reliably calculate an approximation for a modular form of given weight. As an application we have calculated Belyi maps which realize sporadic groups as the Galois group of three-point ramified cover over $P^1_C$ for all genus zero sporadic groups.