Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 4, w^{2} + w]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} + 3x^{2} - 9x - 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $-1$ |
| 2 | $[2, 2, w^{2} - 2w - 5]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w^{2} + 2w + 17]$ | $\phantom{-}\frac{1}{3}e^{2} + e - 1$ |
| 7 | $[7, 7, -w^{2} + w + 9]$ | $\phantom{-}\frac{1}{3}e^{2} - 1$ |
| 13 | $[13, 13, 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{2} - 4$ |
| 25 | $[25, 5, -3w^{2} + 5w + 19]$ | $-\frac{2}{3}e^{2} + 8$ |
| 27 | $[27, 3, 3]$ | $-e^{2} - 2e + 7$ |
| 29 | $[29, 29, w^{2} + w - 1]$ | $\phantom{-}e + 3$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{3}e^{2} + 2e + 2$ |
| 37 | $[37, 37, 2w^{2} + 6w + 3]$ | $-\frac{2}{3}e^{2} + 2$ |
| 41 | $[41, 41, -6w^{2} - 14w - 3]$ | $-e^{2} - e + 9$ |
| 53 | $[53, 53, -4w^{2} + 6w + 27]$ | $-e^{2} - e + 3$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $-e + 9$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}\frac{7}{3}e^{2} + 3e - 13$ |
| 61 | $[61, 61, -2w^{2} + 2w + 13]$ | $\phantom{-}\frac{1}{3}e^{2} - 3e - 7$ |
| 73 | $[73, 73, w^{2} + 3w + 3]$ | $\phantom{-}e^{2} - 3e - 13$ |
| 97 | $[97, 97, w^{2} + w - 15]$ | $\phantom{-}\frac{4}{3}e^{2} + 2e - 4$ |
| 101 | $[101, 101, w^{2} + 3w - 1]$ | $\phantom{-}4e + 6$ |
| 101 | $[101, 101, w^{2} - w - 11]$ | $-2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $1$ |
| $2$ | $[2, 2, w^{2} - 2w - 5]$ | $-1$ |