Base field 4.4.10512.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - 6x + 1\); narrow class number \(4\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 13x^{2} + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{2}e^{3} + \frac{9}{2}e$ |
| 23 | $[23, 23, w^{2} - 2w - 2]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w^{3} - w^{2} - 6w - 3]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w^{2} + 2w + 5]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w + 2]$ | $\phantom{-}0$ |
| 37 | $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ | $-2e^{2} + 16$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 6w - 2]$ | $-2e^{2} + 16$ |
| 47 | $[47, 47, w^{2} - 2w - 1]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w^{2} - 2w - 6]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 2w - 1]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $\phantom{-}4e^{2} - 26$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 4w + 3]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).