A390078 Number of normal subgroups of the modular group of index 6n.

2, 1, 1, 2, 0, 0, 2, 2, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 3, 0, 1, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 3, 4, 0, 0, 2, 0, 1, 0, 5, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 2, 0, 5, 0, 0, 7, 0, 0

Offset

1,1

Comments

With the exceptions of indices 1, 2, and 3, every finite-index normal subgroup of the modular group has index divisible by 6.

Links

William P. Orrick, Table of n, a(n) for n = 1..250

Marston Conder and Peter Dobcsányi, Normal subgroups of low index in the modular group and other Hecke groups, Combinatorial Group Theory, Discrete Groups, and Number Theory (Benjamin Fine, Anthony M. Gaglione, and Dennis Spellman, eds.), Contemporary Mathematics, vol. 421, Amer. Math. Soc., Providence, RI, (2006), 65-86.

Formula

a(n) = A389830(6*n).

Example

The two normal subgroups of index 6 are the commutator subgroup and the principal congruence subgroup of level 2.

Crossrefs

Cf. A389830 (number of subgroups of the modular group of index n).

Sequence in context: A132401 A104273 A051778 * A057554 A060575 A236074

Adjacent sequences: A390075 A390076 A390077 * A390079 A390080 A390081

Keyword

nonn

Author

William P. Orrick, Oct 23 2025

Status

approved