Base field 3.3.1620.1
Generator \(w\), with minimal polynomial \(x^{3} - 12x - 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 8x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w - 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 3e - 1$ |
| 5 | $[5, 5, -2w^{2} + 3w + 19]$ | $-e + 1$ |
| 7 | $[7, 7, -w^{2} + 2w + 7]$ | $-e^{2} - e + 4$ |
| 13 | $[13, 13, w^{2} - 3w - 5]$ | $\phantom{-}e^{2} + 2e - 3$ |
| 17 | $[17, 17, w^{2} - w - 3]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{3}{2}e^{2} - 10e - 1$ |
| 23 | $[23, 23, -w + 3]$ | $\phantom{-}e^{2} + 3e - 6$ |
| 37 | $[37, 37, 3w + 5]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 3e - 5$ |
| 43 | $[43, 43, w^{2} + 3w + 3]$ | $\phantom{-}e^{3} + e^{2} - 7e$ |
| 47 | $[47, 47, -w^{2} + 3]$ | $\phantom{-}e^{3} - 9e + 2$ |
| 49 | $[49, 7, -w^{2} + 5]$ | $-2e^{3} - 4e^{2} + 13e + 4$ |
| 53 | $[53, 53, -w^{2} + w + 13]$ | $-e^{3} - 2e^{2} + 7e - 4$ |
| 61 | $[61, 61, -w^{2} + 15]$ | $-\frac{3}{2}e^{3} - \frac{1}{2}e^{2} + 10e - 7$ |
| 61 | $[61, 61, w^{2} - 2w - 13]$ | $-3e^{3} - 5e^{2} + 19e + 5$ |
| 61 | $[61, 61, -4w - 5]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{5}{2}e^{2} - 10e - 7$ |
| 67 | $[67, 67, -2w^{2} + 6w + 13]$ | $\phantom{-}e^{3} + e^{2} - 11e - 6$ |
| 73 | $[73, 73, 2w^{2} - 2w - 17]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{1}{2}e^{2} - 14e + 3$ |
| 79 | $[79, 79, -w - 5]$ | $\phantom{-}2e^{3} + 4e^{2} - 8e - 14$ |
| 79 | $[79, 79, 2w^{2} - 4w - 17]$ | $\phantom{-}2e^{3} + e^{2} - 15e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $1$ |