Label |
RSZB label |
RZB label |
CP label |
SZ label |
S label |
Name |
Level |
Index |
Genus |
Rank |
$\Q$-gonality |
Cusps |
$\Q$-cusps |
CM points |
Conductor |
Simple |
Squarefree |
Contains -1 |
Decomposition |
Models |
$j$-points |
Local obstruction |
$\operatorname{GL}_2(\mathbb{Z}/N\mathbb{Z})$-generators |
25.30.0.a.1 |
25.30.0.1 |
|
25A0 |
25A0-25a |
|
$X_0(25)$ |
$25$ |
$30$ |
$0$ |
$0$ |
$1$ |
$6$ |
$2$ |
|
$?$ |
? |
? |
✓ |
not computed |
$1$ |
$27$ |
|
$\begin{bmatrix}12&23\\0&6\end{bmatrix}$, $\begin{bmatrix}17&1\\0&12\end{bmatrix}$ |
25.50.2.a.1 |
25.50.2.1 |
|
25E2 |
|
|
|
$25$ |
$50$ |
$2$ |
$2$ |
$2$ |
$2$ |
$0$ |
✓ |
$5^{8}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}2&12\\5&3\end{bmatrix}$, $\begin{bmatrix}13&2\\3&1\end{bmatrix}$ |
25.60.0.a.1 |
25.60.0.1 |
|
25B0 |
25B0-25a |
|
|
$25$ |
$60$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
✓ |
not computed |
$1$ |
$8$ |
|
$\begin{bmatrix}14&11\\0&23\end{bmatrix}$, $\begin{bmatrix}24&23\\0&14\end{bmatrix}$ |
25.60.0.a.2 |
25.60.0.2 |
|
25B0 |
25B0-25b |
|
|
$25$ |
$60$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
✓ |
not computed |
$1$ |
$8$ |
|
$\begin{bmatrix}4&7\\0&19\end{bmatrix}$, $\begin{bmatrix}18&19\\0&16\end{bmatrix}$ |
25.75.2.a.1 |
25.75.2.1 |
|
25F2 |
|
|
|
$25$ |
$75$ |
$2$ |
$2$ |
$2$ |
$7$ |
$0$ |
✓ |
$5^{8}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}16&0\\15&12\end{bmatrix}$, $\begin{bmatrix}20&24\\18&10\end{bmatrix}$ |
25.100.4.a.1 |
25.100.4.2 |
|
25E4 |
|
|
|
$25$ |
$100$ |
$4$ |
$0$ |
$2 \le \gamma \le 6$ |
$4$ |
$0$ |
|
$5^{16}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}7&8\\12&9\end{bmatrix}$, $\begin{bmatrix}11&4\\16&12\end{bmatrix}$ |
25.100.4.b.1 |
25.100.4.3 |
|
25E4 |
|
|
|
$25$ |
$100$ |
$4$ |
$0$ |
$3 \le \gamma \le 6$ |
$4$ |
$0$ |
|
$5^{16}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}16&14\\6&2\end{bmatrix}$, $\begin{bmatrix}19&21\\19&13\end{bmatrix}$ |
25.100.4.c.1 |
25.100.4.1 |
|
25E4 |
|
|
|
$25$ |
$100$ |
$4$ |
$2$ |
$3 \le \gamma \le 4$ |
$4$ |
$0$ |
|
$5^{16}$ |
|
✓ |
✓ |
$2^{2}$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}20&19\\21&16\end{bmatrix}$, $\begin{bmatrix}22&6\\9&13\end{bmatrix}$ |
25.100.4.d.1 |
25.100.4.4 |
|
25E4 |
|
|
|
$25$ |
$100$ |
$4$ |
$4$ |
$3 \le \gamma \le 4$ |
$4$ |
$0$ |
|
$5^{16}$ |
|
|
✓ |
$2^{2}$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}2&10\\20&22\end{bmatrix}$, $\begin{bmatrix}6&24\\11&12\end{bmatrix}$ |
25.120.0-25.a.1.1 |
25.120.0.2 |
|
25B0 |
|
|
|
$25$ |
$120$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
|
not computed |
|
$8$ |
|
$\begin{bmatrix}4&21\\0&17\end{bmatrix}$, $\begin{bmatrix}11&12\\0&4\end{bmatrix}$ |
25.120.0-25.a.1.2 |
25.120.0.1 |
|
25B0 |
|
|
|
$25$ |
$120$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
|
not computed |
|
$8$ |
|
$\begin{bmatrix}16&14\\0&21\end{bmatrix}$, $\begin{bmatrix}21&11\\0&7\end{bmatrix}$ |
25.120.0-25.a.2.1 |
25.120.0.4 |
|
25B0 |
|
|
|
$25$ |
$120$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
|
not computed |
|
$8$ |
|
$\begin{bmatrix}11&24\\0&6\end{bmatrix}$, $\begin{bmatrix}12&21\\0&19\end{bmatrix}$ |
25.120.0-25.a.2.2 |
25.120.0.3 |
|
25B0 |
|
|
|
$25$ |
$120$ |
$0$ |
$0$ |
$1$ |
$12$ |
$2$ |
|
$?$ |
? |
? |
|
not computed |
|
$8$ |
|
$\begin{bmatrix}16&12\\0&11\end{bmatrix}$, $\begin{bmatrix}23&9\\0&11\end{bmatrix}$ |
25.150.4.a.1 |
25.150.4.2 |
|
25F4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$2 \le \gamma \le 5$ |
$14$ |
$0$ |
|
$5^{16}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}8&0\\15&11\end{bmatrix}$, $\begin{bmatrix}13&20\\5&17\end{bmatrix}$ |
25.150.4.b.1 |
25.150.4.1 |
|
25F4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$3 \le \gamma \le 4$ |
$14$ |
$5$ |
|
$5^{8}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$1$ |
|
$\begin{bmatrix}4&5\\20&7\end{bmatrix}$, $\begin{bmatrix}13&0\\5&7\end{bmatrix}$ |
25.150.4.c.1 |
25.150.4.3 |
|
25F4 |
|
|
|
$25$ |
$150$ |
$4$ |
$4$ |
$3 \le \gamma \le 4$ |
$14$ |
$0$ |
|
$5^{16}$ |
|
|
✓ |
$2^{2}$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}3&15\\20&4\end{bmatrix}$, $\begin{bmatrix}7&20\\15&7\end{bmatrix}$ |
25.150.4.d.1 |
25.150.4.4 |
|
25F4 |
|
|
|
$25$ |
$150$ |
$4$ |
$4$ |
$3 \le \gamma \le 4$ |
$14$ |
$0$ |
✓ |
$5^{16}$ |
|
✓ |
✓ |
$2^{2}$ |
$2$ |
$0$ |
|
$\begin{bmatrix}13&22\\9&7\end{bmatrix}$, $\begin{bmatrix}17&7\\15&8\end{bmatrix}$ |
25.150.4.e.1 |
25.150.4.8 |
|
25G4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$2 \le \gamma \le 5$ |
$14$ |
$0$ |
|
$5^{16}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}2&21\\0&22\end{bmatrix}$, $\begin{bmatrix}21&4\\0&12\end{bmatrix}$ |
25.150.4.e.2 |
25.150.4.9 |
|
25G4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$2 \le \gamma \le 5$ |
$14$ |
$0$ |
|
$5^{16}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}21&23\\0&23\end{bmatrix}$, $\begin{bmatrix}22&23\\0&23\end{bmatrix}$ |
25.150.4.f.1 |
25.150.4.5 |
|
25G4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$3 \le \gamma \le 4$ |
$14$ |
$5$ |
|
$5^{8}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$1$ |
|
$\begin{bmatrix}18&6\\0&8\end{bmatrix}$, $\begin{bmatrix}24&10\\0&13\end{bmatrix}$ |
25.150.4.f.2 |
25.150.4.6 |
|
25G4 |
|
|
|
$25$ |
$150$ |
$4$ |
$0$ |
$3 \le \gamma \le 4$ |
$14$ |
$5$ |
|
$5^{8}$ |
✓ |
✓ |
✓ |
$4$ |
$2$ |
$1$ |
|
$\begin{bmatrix}7&4\\0&7\end{bmatrix}$, $\begin{bmatrix}8&3\\0&24\end{bmatrix}$ |
25.150.4.g.1 |
25.150.4.7 |
|
25G4 |
|
|
|
$25$ |
$150$ |
$4$ |
$4$ |
$3 \le \gamma \le 5$ |
$14$ |
$0$ |
|
$5^{16}$ |
|
|
✓ |
$2^{2}$ |
$2$ |
$0$ |
✓ |
$\begin{bmatrix}3&11\\0&3\end{bmatrix}$, $\begin{bmatrix}9&20\\0&12\end{bmatrix}$ |
25.150.8.a.1 |
25.150.8.1 |
|
25A8 |
|
|
|
$25$ |
$150$ |
$8$ |
$2$ |
$3 \le \gamma \le 4$ |
$10$ |
$2$ |
|
$5^{24}$ |
|
✓ |
✓ |
$2^{2}\cdot4$ |
$2$ |
$1$ |
|
$\begin{bmatrix}8&0\\0&14\end{bmatrix}$, $\begin{bmatrix}11&10\\0&13\end{bmatrix}$ |
25.150.10.a.1 |
25.150.10.1 |
|
25A10 |
|
|
|
$25$ |
$150$ |
$10$ |
$10$ |
$4 \le \gamma \le 5$ |
$6$ |
$0$ |
✓ |
$5^{40}$ |
|
✓ |
✓ |
$2\cdot8$ |
$1$ |
$0$ |
|
$\begin{bmatrix}8&12\\24&12\end{bmatrix}$, $\begin{bmatrix}21&1\\10&24\end{bmatrix}$ |
25.250.14.a.1 |
25.250.14.1 |
|
25A14 |
|
|
$X_{\mathrm{ns}}^+(25)$ |
$25$ |
$250$ |
$14$ |
$14$ |
$5 \le \gamma \le 14$ |
$10$ |
$0$ |
✓ |
$5^{56}$ |
|
✓ |
✓ |
$2^{3}\cdot8$ |
$1$ |
$0$ |
|
$\begin{bmatrix}5&21\\16&20\end{bmatrix}$, $\begin{bmatrix}11&9\\23&14\end{bmatrix}$ |
25.300.12.a.1 |
25.300.12.4 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}7&20\\5&24\end{bmatrix}$, $\begin{bmatrix}16&10\\10&19\end{bmatrix}$ |
25.300.12.b.1 |
25.300.12.3 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}19&20\\0&23\end{bmatrix}$, $\begin{bmatrix}21&20\\5&12\end{bmatrix}$ |
25.300.12.c.1 |
25.300.12.2 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{32}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}18&20\\5&1\end{bmatrix}$, $\begin{bmatrix}24&10\\20&4\end{bmatrix}$ |
25.300.12.d.1 |
25.300.12.1 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$10$ |
|
$5^{24}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$1$ |
|
$\begin{bmatrix}4&20\\15&24\end{bmatrix}$, $\begin{bmatrix}17&0\\15&24\end{bmatrix}$ |
25.300.12.e.1 |
25.300.12.5 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$4$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
|
✓ |
$2^{2}\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}1&5\\20&18\end{bmatrix}$, $\begin{bmatrix}14&15\\10&23\end{bmatrix}$ |
25.300.12.f.1 |
25.300.12.6 |
|
25A12 |
|
|
|
$25$ |
$300$ |
$12$ |
$4$ |
$5 \le \gamma \le 8$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$2^{2}\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}3&11\\19&12\end{bmatrix}$, $\begin{bmatrix}9&8\\17&6\end{bmatrix}$ |
25.300.12.g.1 |
25.300.12.11 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}1&1\\0&18\end{bmatrix}$, $\begin{bmatrix}14&10\\0&6\end{bmatrix}$ |
25.300.12.g.2 |
25.300.12.15 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}2&22\\0&21\end{bmatrix}$, $\begin{bmatrix}12&14\\0&19\end{bmatrix}$ |
25.300.12.h.1 |
25.300.12.16 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}13&0\\0&4\end{bmatrix}$, $\begin{bmatrix}17&4\\0&16\end{bmatrix}$ |
25.300.12.h.2 |
25.300.12.10 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}9&9\\0&8\end{bmatrix}$, $\begin{bmatrix}21&13\\0&12\end{bmatrix}$ |
25.300.12.i.1 |
25.300.12.12 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{32}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}1&17\\0&14\end{bmatrix}$, $\begin{bmatrix}18&19\\0&21\end{bmatrix}$ |
25.300.12.i.2 |
25.300.12.8 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{32}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}4&15\\0&18\end{bmatrix}$, $\begin{bmatrix}16&8\\0&7\end{bmatrix}$ |
25.300.12.j.1 |
25.300.12.7 |
|
25B12 |
|
|
$X_{\pm1}(25)$ |
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$10$ |
|
$5^{24}$ |
|
✓ |
✓ |
$4\cdot8$ |
$2$ |
$1$ |
|
$\begin{bmatrix}1&15\\0&17\end{bmatrix}$, $\begin{bmatrix}24&23\\0&17\end{bmatrix}$ |
25.300.12.j.2 |
25.300.12.13 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$0$ |
$4 \le \gamma \le 5$ |
$28$ |
$10$ |
|
$5^{24}$ |
|
✓ |
✓ |
$4\cdot8$ |
$1$ |
$1$ |
|
$\begin{bmatrix}21&13\\0&24\end{bmatrix}$, $\begin{bmatrix}23&12\\0&24\end{bmatrix}$ |
25.300.12.k.1 |
25.300.12.9 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$4$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
|
✓ |
$2^{2}\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}11&8\\0&23\end{bmatrix}$, $\begin{bmatrix}19&12\\0&8\end{bmatrix}$ |
25.300.12.k.2 |
25.300.12.14 |
|
25B12 |
|
|
|
$25$ |
$300$ |
$12$ |
$4$ |
$4 \le \gamma \le 5$ |
$28$ |
$0$ |
|
$5^{48}$ |
|
|
✓ |
$2^{2}\cdot8$ |
$1$ |
$0$ |
✓ |
$\begin{bmatrix}6&21\\0&19\end{bmatrix}$, $\begin{bmatrix}17&14\\0&6\end{bmatrix}$ |
25.300.16.a.1 |
25.300.16.1 |
|
25A16 |
|
|
|
$25$ |
$300$ |
$16$ |
$2$ |
$5$ |
$20$ |
$2$ |
|
$5^{48}$ |
|
✓ |
✓ |
$2^{2}\cdot4^{3}$ |
|
$0$ |
|
$\begin{bmatrix}9&10\\0&6\end{bmatrix}$, $\begin{bmatrix}16&20\\0&13\end{bmatrix}$ |
25.300.16.a.2 |
25.300.16.2 |
|
25A16 |
|
|
|
$25$ |
$300$ |
$16$ |
$2$ |
$5$ |
$20$ |
$2$ |
|
$5^{48}$ |
|
✓ |
✓ |
$2^{2}\cdot4^{3}$ |
|
$0$ |
|
$\begin{bmatrix}7&0\\0&16\end{bmatrix}$, $\begin{bmatrix}9&10\\0&14\end{bmatrix}$ |
25.300.20.a.1 |
25.300.20.2 |
|
25A20 |
|
|
|
$25$ |
$300$ |
$20$ |
$0$ |
$5 \le \gamma \le 10$ |
$12$ |
$0$ |
|
$5^{80}$ |
|
✓ |
✓ |
$4\cdot16$ |
|
$0$ |
✓ |
$\begin{bmatrix}17&20\\0&7\end{bmatrix}$, $\begin{bmatrix}21&12\\18&4\end{bmatrix}$, $\begin{bmatrix}24&13\\22&11\end{bmatrix}$ |
25.300.20.b.1 |
25.300.20.3 |
|
25A20 |
|
|
|
$25$ |
$300$ |
$20$ |
$0$ |
$5 \le \gamma \le 10$ |
$12$ |
$0$ |
|
$5^{80}$ |
|
✓ |
✓ |
$4\cdot16$ |
|
$0$ |
✓ |
$\begin{bmatrix}3&16\\14&7\end{bmatrix}$, $\begin{bmatrix}16&12\\18&14\end{bmatrix}$, $\begin{bmatrix}19&20\\5&9\end{bmatrix}$ |
25.300.20.c.1 |
25.300.20.1 |
|
25A20 |
|
|
|
$25$ |
$300$ |
$20$ |
$10$ |
$5 \le \gamma \le 10$ |
$12$ |
$0$ |
|
$5^{80}$ |
|
✓ |
✓ |
$2^{2}\cdot8^{2}$ |
|
$0$ |
✓ |
$\begin{bmatrix}16&10\\10&16\end{bmatrix}$, $\begin{bmatrix}24&23\\22&16\end{bmatrix}$ |
25.300.20.d.1 |
25.300.20.4 |
|
25A20 |
|
|
|
$25$ |
$300$ |
$20$ |
$20$ |
$5 \le \gamma \le 10$ |
$12$ |
$0$ |
|
$5^{80}$ |
|
|
✓ |
$2^{2}\cdot8^{2}$ |
|
$0$ |
✓ |
$\begin{bmatrix}6&20\\20&6\end{bmatrix}$, $\begin{bmatrix}16&17\\8&9\end{bmatrix}$, $\begin{bmatrix}22&10\\20&17\end{bmatrix}$ |
25.375.22.a.1 |
25.375.22.1 |
|
25A22 |
|
|
$X_{\mathrm{sp}}^+(25)$ |
$25$ |
$375$ |
$22$ |
$16$ |
$7 \le \gamma \le 20$ |
$15$ |
$1$ |
✓ |
$5^{80}$ |
|
✓ |
✓ |
$2^{5}\cdot4\cdot8$ |
|
$0$ |
|
$\begin{bmatrix}0&2\\17&0\end{bmatrix}$, $\begin{bmatrix}0&7\\24&0\end{bmatrix}$ |
25.500.32.a.1 |
25.500.32.2 |
|
|
|
|
$X_{\mathrm{ns}}(25)$ |
$25$ |
$500$ |
$32$ |
$14$ |
$9 \le \gamma \le 28$ |
$20$ |
$0$ |
|
$5^{128}$ |
|
✓ |
✓ |
$2^{4}\cdot8^{3}$ |
|
$0$ |
✓ |
$\begin{bmatrix}11&0\\0&11\end{bmatrix}$, $\begin{bmatrix}17&6\\19&11\end{bmatrix}$ |
25.500.32.b.1 |
25.500.32.1 |
|
|
|
|
|
$25$ |
$500$ |
$32$ |
$24$ |
$9 \le \gamma \le 28$ |
$20$ |
$0$ |
|
$5^{128}$ |
|
|
✓ |
$2^{4}\cdot8^{3}$ |
|
$0$ |
✓ |
$\begin{bmatrix}16&9\\18&9\end{bmatrix}$, $\begin{bmatrix}21&16\\9&5\end{bmatrix}$ |