Higher Levels

Abstract

Let Γ = SL₂(Z) again. We define Γ_N (or Γ(N)) for each positive integer N to be the subgroup of Γ consisting of those matrices satisfying the condition

$$\left({\begin{array}{*{20}{c}}a&b \\c&d \end{array}} \right)\,\, \equiv \,\,1\,\,\,\,(\bmod N),$$

in other words

$$a\,\, \equiv \,\,d\,\, \equiv\,\,1\,\,\,\,(\bmod\,N)\,\,\,\,\,\,\,and\,\,\,\,\,\,\,c\,\, \equiv \,\,b\,\, \equiv \,\,0\,\,\,\,(\bmod \,N).$$

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