Congruence Subgroup

class sage.modular.arithgroup.congroup_gamma.Gamma_class(level)

Bases: sage.modular.arithgroup.congroup_generic.CongruenceSubgroup

The principal congruence subgroup .

index()

Return the index of self in the full modular group. This is given by

EXAMPLE::

sage: [Gamma(n).index() for n in [1..19]] [1, 6, 24, 48, 120, 144, 336, 384, 648, 720, 1320, 1152, 2184, 2016, 2880, 3072, 4896, 3888, 6840] sage: Gamma(32041).index() 32893086819240

sage.modular.arithgroup.congroup_gamma.Gamma_constructor(N)

Return the congruence subgroup .

EXAMPLES:

sage: Gamma(5) # indirect doctest
Congruence Subgroup Gamma(5)
sage: G = Gamma(23)
sage: G is Gamma(23)
True
sage: G == loads(dumps(G))
True
sage: G is loads(dumps(G))
True

sage.modular.arithgroup.congroup_gamma.is_Gamma(x)

Return True if x is a congruence subgroup of type Gamma.

EXAMPLES:

sage: from sage.modular.arithgroup.all import is_Gamma
sage: is_Gamma(Gamma0(13))
False
sage: is_Gamma(Gamma(4))
True