Base field 4.4.18688.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17,17,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{11}{3}]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 21x^{16} + 182x^{14} - 841x^{12} + 2228x^{10} - 3370x^{8} + 2702x^{6} - 935x^{4} + 60x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ | $\phantom{-}e^{17} - 21e^{15} + 182e^{13} - 840e^{11} + 2214e^{9} - 3299e^{7} + 2543e^{5} - 784e^{3} + 13e$ |
| 7 | $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ | $-2e^{17} + 42e^{15} - 364e^{13} + 1681e^{11} - 4442e^{9} + 6669e^{7} - 5245e^{5} + 1718e^{3} - 69e$ |
| 9 | $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ | $\phantom{-}e^{14} - 18e^{12} + 128e^{10} - 457e^{8} + 857e^{6} - 798e^{4} + 299e^{2} - 12$ |
| 9 | $[9, 3, w + 1]$ | $\phantom{-}e^{14} - 18e^{12} + 128e^{10} - 456e^{8} + 846e^{6} - 761e^{4} + 261e^{2} - 9$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}e^{16} - 20e^{14} + 164e^{12} - 712e^{10} + 1758e^{8} - 2454e^{6} + 1791e^{4} - 546e^{2} + 18$ |
| 17 | $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ | $\phantom{-}1$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ | $\phantom{-}2e^{17} - 44e^{15} + 400e^{13} - 1938e^{11} + 5369e^{9} - 8442e^{7} + 6954e^{5} - 2405e^{3} + 117e$ |
| 31 | $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ | $-e^{17} + 23e^{15} - 219e^{13} + 1112e^{11} - 3225e^{9} + 5289e^{7} - 4503e^{5} + 1559e^{3} - 40e$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ | $-2e^{16} + 37e^{14} - 274e^{12} + 1042e^{10} - 2172e^{8} + 2465e^{6} - 1437e^{4} + 360e^{2} - 14$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}2e^{16} - 39e^{14} + 310e^{12} - 1296e^{10} + 3058e^{8} - 4040e^{6} + 2746e^{4} - 751e^{2} + 21$ |
| 41 | $[41, 41, 2w + 3]$ | $-e^{16} + 17e^{14} - 110e^{12} + 328e^{10} - 388e^{8} - 105e^{6} + 559e^{4} - 301e^{2} + 8$ |
| 41 | $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ | $-e^{16} + 18e^{14} - 127e^{12} + 440e^{10} - 748e^{8} + 474e^{6} + 139e^{4} - 203e^{2} + 6$ |
| 47 | $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ | $-e^{17} + 18e^{15} - 127e^{13} + 441e^{11} - 760e^{9} + 522e^{7} + 68e^{5} - 181e^{3} + 19e$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ | $-5e^{17} + 105e^{15} - 908e^{13} + 4173e^{11} - 10943e^{9} + 16259e^{7} - 12610e^{5} + 4021e^{3} - 120e$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ | $-2e^{16} + 38e^{14} - 290e^{12} + 1139e^{10} - 2447e^{8} + 2817e^{6} - 1574e^{4} + 331e^{2} - 17$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ | $-e^{16} + 21e^{14} - 184e^{12} + 870e^{10} - 2382e^{8} + 3735e^{6} - 3068e^{4} + 1035e^{2} - 36$ |
| 73 | $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ | $\phantom{-}e^{14} - 19e^{12} + 142e^{10} - 528e^{8} + 1015e^{6} - 941e^{4} + 330e^{2} - 10$ |
| 73 | $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ | $\phantom{-}e^{16} - 18e^{14} + 128e^{12} - 458e^{10} + 872e^{8} - 879e^{6} + 481e^{4} - 155e^{2} + 16$ |
| 103 | $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ | $\phantom{-}8e^{17} - 168e^{15} + 1455e^{13} - 6712e^{11} + 17724e^{9} - 26643e^{7} + 21058e^{5} - 6935e^{3} + 251e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,\frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + \frac{11}{3}]$ | $-1$ |