Base field 4.4.18432.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 18\); 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: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 10x^{4} + 18x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $\phantom{-}e^{4} - 9e^{2} + 8$ |
| 7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $\phantom{-}e^{4} - 9e^{2} + 8$ |
| 7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $\phantom{-}e^{4} - 9e^{2} + 8$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $\phantom{-}e^{4} - 9e^{2} + 8$ |
| 9 | $[9, 3, w - 3]$ | $\phantom{-}\frac{3}{2}e^{5} - 13e^{3} + 11e$ |
| 41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $-\frac{5}{2}e^{5} + 23e^{3} - 27e$ |
| 41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $-\frac{5}{2}e^{5} + 23e^{3} - 27e$ |
| 41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $-\frac{5}{2}e^{5} + 23e^{3} - 27e$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $-\frac{5}{2}e^{5} + 23e^{3} - 27e$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $\phantom{-}2e^{5} - 18e^{3} + 16e$ |
| 47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $\phantom{-}2e^{5} - 18e^{3} + 16e$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $\phantom{-}2e^{5} - 18e^{3} + 16e$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}2e^{5} - 18e^{3} + 16e$ |
| 89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $-\frac{1}{2}e^{5} + 3e^{3} + 7e$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $-\frac{1}{2}e^{5} + 3e^{3} + 7e$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $-\frac{1}{2}e^{5} + 3e^{3} + 7e$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $-\frac{1}{2}e^{5} + 3e^{3} + 7e$ |
| 97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $\phantom{-}e^{4} - 6e^{2} - 2$ |
| 97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $\phantom{-}e^{4} - 6e^{2} - 2$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).