8
votes
3answers
512 views

Congruence Subgroups as Open Subgroups of the Modular Group Under the Right Topology

It occurred to me that a subgroup of the modular group $\Gamma$ is a congruence subgroup iff it contains a subgroup of the form $\Gamma(N)$, while a subgroup of a general topological group is open iff ...
15
votes
2answers
1k views

Distinguishing congruence subgroups of the modular group

This question is something of a follow-up to Transformation formulae for classical theta functions . How does one recognise whether a subgroup of the modular group $\Gamma=\mathrm{SL}_2(\mathbb{Z})$ ...