Base field 3.3.1384.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[4, 2, -w^{2} + 8]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 31\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} - w + 11]$ | $\phantom{-}2e^{2} - 13$ |
| 11 | $[11, 11, 2w^{2} + 2w - 15]$ | $-e^{3} + 6e$ |
| 11 | $[11, 11, w^{2} + w - 9]$ | $-e^{3} + 7e$ |
| 13 | $[13, 13, 2w - 5]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{2} - w + 5]$ | $\phantom{-}e^{3} - 7e$ |
| 27 | $[27, 3, -3]$ | $-e^{2} + 5$ |
| 29 | $[29, 29, w^{2} + w - 3]$ | $-3e^{2} + 19$ |
| 37 | $[37, 37, -2w^{2} + 15]$ | $\phantom{-}2e$ |
| 43 | $[43, 43, 3w^{2} + w - 27]$ | $-2e^{2} + 6$ |
| 49 | $[49, 7, -w^{2} + w + 3]$ | $-e^{3} + 7e$ |
| 67 | $[67, 67, 2w^{2} + 2w - 17]$ | $\phantom{-}e^{3} - 9e$ |
| 71 | $[71, 71, 2w - 1]$ | $-4e^{2} + 26$ |
| 79 | $[79, 79, 3w^{2} + w - 25]$ | $\phantom{-}2e^{3} - 11e$ |
| 83 | $[83, 83, w^{2} + 3w - 5]$ | $\phantom{-}4e^{2} - 30$ |
| 89 | $[89, 89, -4w^{2} - 4w + 31]$ | $-e^{3} + 6e$ |
| 89 | $[89, 89, -2w^{2} + 17]$ | $\phantom{-}3e^{2} - 23$ |
| 89 | $[89, 89, 2w^{2} + 2w - 19]$ | $\phantom{-}6e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 2]$ | $-1$ |