Base field \(\Q(\sqrt{281}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10,10,59w + 465]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $53$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 18x^{10} + 117x^{8} - 2x^{7} - 336x^{6} + 18x^{5} + 422x^{4} - 61x^{3} - 204x^{2} + 47x + 15\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 8]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w + 9]$ | $-1$ |
| 5 | $[5, 5, -76w + 675]$ | $\phantom{-}1$ |
| 5 | $[5, 5, 76w + 599]$ | $\phantom{-}12e^{11} + 11e^{10} - 206e^{9} - 189e^{8} + 1232e^{7} + 1107e^{6} - 3023e^{5} - 2558e^{4} + 2728e^{3} + 1763e^{2} - 836e - 195$ |
| 7 | $[7, 7, -8w - 63]$ | $-e^{11} + 20e^{9} + 6e^{8} - 139e^{7} - 75e^{6} + 383e^{5} + 260e^{4} - 354e^{3} - 205e^{2} + 108e + 23$ |
| 7 | $[7, 7, -8w + 71]$ | $\phantom{-}6e^{11} + 6e^{10} - 102e^{9} - 101e^{8} + 603e^{7} + 578e^{6} - 1463e^{5} - 1307e^{4} + 1311e^{3} + 897e^{2} - 399e - 100$ |
| 9 | $[9, 3, 3]$ | $-14e^{11} - 13e^{10} + 239e^{9} + 221e^{8} - 1420e^{7} - 1279e^{6} + 3462e^{5} + 2925e^{4} - 3113e^{3} - 2013e^{2} + 948e + 226$ |
| 17 | $[17, 17, 42w + 331]$ | $-21e^{11} - 21e^{10} + 356e^{9} + 351e^{8} - 2098e^{7} - 1991e^{6} + 5079e^{5} + 4459e^{4} - 4564e^{3} - 3030e^{2} + 1401e + 330$ |
| 17 | $[17, 17, 42w - 373]$ | $-14e^{11} - 13e^{10} + 241e^{9} + 225e^{8} - 1445e^{7} - 1329e^{6} + 3547e^{5} + 3094e^{4} - 3177e^{3} - 2140e^{2} + 964e + 237$ |
| 29 | $[29, 29, -6w - 47]$ | $\phantom{-}10e^{11} + 9e^{10} - 173e^{9} - 157e^{8} + 1044e^{7} + 936e^{6} - 2584e^{5} - 2201e^{4} + 2342e^{3} + 1538e^{2} - 721e - 174$ |
| 29 | $[29, 29, 6w - 53]$ | $\phantom{-}18e^{11} + 16e^{10} - 312e^{9} - 281e^{8} + 1886e^{7} + 1687e^{6} - 4668e^{5} - 3988e^{4} + 4207e^{3} + 2779e^{2} - 1280e - 306$ |
| 31 | $[31, 31, 10w + 79]$ | $-19e^{11} - 18e^{10} + 324e^{9} + 305e^{8} - 1922e^{7} - 1759e^{6} + 4676e^{5} + 4010e^{4} - 4191e^{3} - 2759e^{2} + 1271e + 311$ |
| 31 | $[31, 31, -10w + 89]$ | $-21e^{11} - 21e^{10} + 355e^{9} + 350e^{8} - 2084e^{7} - 1978e^{6} + 5018e^{5} + 4412e^{4} - 4473e^{3} - 2984e^{2} + 1360e + 320$ |
| 43 | $[43, 43, 2w - 19]$ | $\phantom{-}39e^{11} + 36e^{10} - 668e^{9} - 616e^{8} + 3983e^{7} + 3591e^{6} - 9734e^{5} - 8259e^{4} + 8730e^{3} + 5668e^{2} - 2647e - 622$ |
| 43 | $[43, 43, -2w - 17]$ | $\phantom{-}40e^{11} + 38e^{10} - 684e^{9} - 647e^{8} + 4072e^{7} + 3752e^{6} - 9949e^{5} - 8593e^{4} + 8964e^{3} + 5913e^{2} - 2752e - 655$ |
| 53 | $[53, 53, 194w + 1529]$ | $\phantom{-}46e^{11} + 43e^{10} - 786e^{9} - 732e^{8} + 4674e^{7} + 4243e^{6} - 11399e^{5} - 9713e^{4} + 10233e^{3} + 6675e^{2} - 3110e - 744$ |
| 53 | $[53, 53, -194w + 1723]$ | $-e^{11} - e^{10} + 18e^{9} + 18e^{8} - 115e^{7} - 112e^{6} + 311e^{5} + 279e^{4} - 330e^{3} - 220e^{2} + 121e + 30$ |
| 59 | $[59, 59, -110w - 867]$ | $\phantom{-}7e^{11} + 8e^{10} - 115e^{9} - 127e^{8} + 651e^{7} + 674e^{6} - 1508e^{5} - 1401e^{4} + 1313e^{3} + 898e^{2} - 398e - 84$ |
| 59 | $[59, 59, 110w - 977]$ | $-18e^{11} - 20e^{10} + 300e^{9} + 324e^{8} - 1733e^{7} - 1768e^{6} + 4124e^{5} + 3804e^{4} - 3711e^{3} - 2545e^{2} + 1156e + 276$ |
| 79 | $[79, 79, 650w - 5773]$ | $-38e^{11} - 34e^{10} + 655e^{9} + 589e^{8} - 3935e^{7} - 3482e^{6} + 9690e^{5} + 8113e^{4} - 8733e^{3} - 5597e^{2} + 2650e + 614$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 9]$ | $1$ |
| $5$ | $[5,5,-76w + 675]$ | $-1$ |