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The level of an open subgroup $H$ of $\GL(2,\widehat\Z)$ is the least positive integer $N$ for which $H$ is equal to the inverse image of its projection to $\GL(2,\Z/N\Z)$.

This also applies to open subgroups of $\GL(2,\Z_\ell)$, in which case $N$ is necessarily a power of $\ell$.

Knowl status:
  • Review status: beta
  • Last edited by Andrew Sutherland on 2021-07-17 11:30:07
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