Base field 4.4.9248.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 11x^{4} + 26x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{4}e^{3} + \frac{11}{2}e$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 6e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 6e$ |
| 19 | $[19, 19, -w^{3} + 3w + 1]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$ |
| 19 | $[19, 19, -w^{3} + 3w - 1]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 13e$ |
| 43 | $[43, 43, -w^{2} + w - 1]$ | $-e^{4} + 7e^{2} - 2$ |
| 43 | $[43, 43, w^{2} + w + 1]$ | $-e^{4} + 7e^{2} - 2$ |
| 49 | $[49, 7, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$ |
| 49 | $[49, 7, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 9w + 3]$ | $-e^{4} + 9e^{2} - 10$ |
| 53 | $[53, 53, 2w^{3} + w^{2} - 9w - 3]$ | $-e^{4} + 9e^{2} - 10$ |
| 59 | $[59, 59, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e^{4} - 11e^{2} + 14$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 4w + 1]$ | $\phantom{-}e^{4} - 11e^{2} + 14$ |
| 67 | $[67, 67, 3w^{3} - 13w + 1]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{29}{2}e^{3} + 21e$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 6w - 5]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{29}{2}e^{3} + 21e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{4} - 9e^{2} + 18$ |
| 83 | $[83, 83, -2w^{3} - w^{2} + 9w + 7]$ | $\phantom{-}e^{4} - 7e^{2} + 2$ |
| 83 | $[83, 83, 4w^{3} - 18w - 1]$ | $\phantom{-}e^{4} - 7e^{2} + 2$ |
| 89 | $[89, 89, -2w^{3} + 10w + 1]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 2e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).