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: | $[9, 3, w - 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ | $-2$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ | $-2$ |
| 7 | $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ | $-2$ |
| 7 | $[7, 7, \frac{1}{3}w^{2} + w - 1]$ | $-2$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ | $-2$ |
| 9 | $[9, 3, w - 3]$ | $-1$ |
| 41 | $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ | $\phantom{-}2$ |
| 41 | $[41, 41, \frac{1}{3}w^{2} + w - 3]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ | $\phantom{-}2$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ | $-12$ |
| 47 | $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ | $-12$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $-12$ |
| 47 | $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $-12$ |
| 89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ | $-10$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} + w - 5]$ | $-10$ |
| 89 | $[89, 89, \frac{2}{3}w^{2} - w - 5]$ | $-10$ |
| 89 | $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ | $-10$ |
| 97 | $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ | $-2$ |
| 97 | $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ | $-2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w - 3]$ | $1$ |