For an open subgroup $H$ of $\GL_2(\widehat \Z)$, the **cusps** of $H$ are the double cosets $\SL_2(\widehat \Z)\backslash \bigl(\pm H \cap \SL_2(\widehat \Z)\bigr)/\langle \delta\rangle$, where $
\delta := \begin{bmatrix}1&1\\0&1\end{bmatrix}$. These correspond to the cusps of the modular curve $X_H$.

The **width** of a cusp is the number of right cosets it contains. The sum of the cusp widths is equal to the $\PSL_2$-index of $H$.

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- Last edited by Andrew Sutherland on 2022-12-12 07:15:04

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- 2022-12-12 07:15:04 by Andrew Sutherland
- 2022-12-12 07:11:11 by Andrew Sutherland
- 2022-12-12 06:31:46 by Andrew Sutherland
- 2022-12-12 06:30:55 by Andrew Sutherland
- 2022-12-12 06:29:49 by Andrew Sutherland
- 2022-12-12 06:29:01 by Andrew Sutherland
- 2022-12-12 06:28:23 by Andrew Sutherland
- 2022-12-12 06:24:14 by Andrew Sutherland
- 2022-12-12 06:23:11 by Andrew Sutherland
- 2022-12-12 05:57:48 by Andrew Sutherland
- 2022-11-29 07:45:55 by Andrew Sutherland

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