modular group

Let q be a positive integer, then Γ_0(q) is defined as the set of all matrices [a | b c | d] in the modular group Γ Γ with c congruent 0 (mod q). Γ_0(q) is a subgroup of Γ. For any prime p, the set R_Γ union union _(k = 0)^(p - 1) S T^k(R_Γ) is a fundamental region of the subgroup Γ_0(q), where S τ = - 1/τ and T τ = τ + 1.

modular group Γ | modular group Λ | supersingular prime