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The group $\Gamma_1(N)$ is the subgroup of $\textrm{SL}(2,\mathbb{Z})$ that consists of matrices that become upper triangular with ones on the diagonal when reduced modulo $N$. That is, \[ \Gamma_1(N) = \left\lbrace \left .\begin{pmatrix} a & b \\ c & d \end{pmatrix}\in \textrm{SL}(2,\mathbb{Z})\ \right|\ a\equiv 1,\ c\equiv 0,\ d\equiv 1\pmod N \right\rbrace. \]

Knowl status:
  • Review status: beta
  • Last edited by John Jones on 2012-04-18 07:11:47
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