Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{3} + w^{2} - 6w - 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 16x^{12} + 101x^{10} - 318x^{8} + 519x^{6} - 411x^{4} + 124x^{2} - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $-e^{10} + 11e^{8} - 42e^{6} + 65e^{4} - 36e^{2} + 2$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $-e^{11} + 12e^{9} - 51e^{7} + 90e^{5} - 57e^{3} + 5e$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $\phantom{-}e^{11} - 12e^{9} + 52e^{7} - 98e^{5} + 77e^{3} - 21e$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}e^{13} - 15e^{11} + 87e^{9} - 244e^{7} + 338e^{5} - 212e^{3} + 47e$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-e^{13} + 15e^{11} - 87e^{9} + 243e^{7} - 330e^{5} + 192e^{3} - 32e$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $-e^{11} + 11e^{9} - 43e^{7} + 73e^{5} - 55e^{3} + 16e$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $-e^{13} + 15e^{11} - 87e^{9} + 243e^{7} - 326e^{5} + 171e^{3} - 12e$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}e^{13} - 12e^{11} + 49e^{9} - 63e^{7} - 68e^{5} + 223e^{3} - 130e$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $-e^{12} + 16e^{10} - 96e^{8} + 267e^{6} - 338e^{4} + 151e^{2} - 2$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-e^{13} + 13e^{11} - 62e^{9} + 128e^{7} - 91e^{5} - 32e^{3} + 48e$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $\phantom{-}e^{13} - 13e^{11} + 64e^{9} - 151e^{7} + 181e^{5} - 108e^{3} + 27e$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $\phantom{-}e^{12} - 15e^{10} + 86e^{8} - 232e^{6} + 284e^{4} - 111e^{2} - 12$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-2e^{11} + 26e^{9} - 127e^{7} + 282e^{5} - 265e^{3} + 71e$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $\phantom{-}2e^{12} - 23e^{10} + 94e^{8} - 165e^{6} + 127e^{4} - 51e^{2} + 10$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $\phantom{-}2e^{13} - 29e^{11} + 163e^{9} - 446e^{7} + 608e^{5} - 372e^{3} + 75e$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $-e^{12} + 10e^{10} - 29e^{8} + 7e^{6} + 60e^{4} - 28e^{2} - 12$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $-e^{13} + 16e^{11} - 95e^{9} + 253e^{7} - 275e^{5} + 45e^{3} + 55e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}2e^{10} - 22e^{8} + 86e^{6} - 141e^{4} + 82e^{2} - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $-1$ |