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 $\ell$.

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**Knowl status:**

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

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**History:**(expand/hide all)

- 2021-07-17 11:30:07 by Andrew Sutherland
- 2021-07-17 11:29:06 by Andrew Sutherland
- 2021-07-17 11:26:28 by Andrew Sutherland

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