Experimental finding of modular forms for noncongruence subgroups

Details Experimental finding of modular forms for noncongruence subgroups Experimental finding of modular forms for noncongruence subgroups

2009-10-05

arxiv.org/abs/0910.0739v1

Mathematics

Number Theory

12 pages

Scientific paper

In this paper we will use experimental and computational methods to find
modular forms for non-congruence subgroups, and the modular forms for
congruence subgroups that they are associated with via the
Atkin--Swinnerton-Dyer correspondence. We also prove a generalization of a
criterion due to Ligozat for an eta-quotient to be a modular function.

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