Glossary

Here are some terms that are non-trivial.

Congruence Subgroup

Any subgroup of the modular group which contains some principal congruence subgroup.

Elliptic (of matrices)

A Möbius transformation whose fixed points are exactly two distinct complex conjugate points.

Modular Group

The set of 2×2 matrices with integer entries and determinant 1. In many applications elements of the modular group are identified with their negatives and/or determinants of -1 are allowed as well.

Principal Congruence Subgroup of Level m

The subgroup of the modular group whose elements are all congruent to the identity modulus some natural number n. Note that the principal congruence subgroup of level 1 is the entire modular group.