Base field 4.4.18097.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 9, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 10x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ | $\phantom{-}2$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}$ |
| 17 | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ | $-\frac{5}{2}e^{3} + \frac{49}{2}e$ |
| 27 | $[27, 3, -w^{3} + 7w + 1]$ | $-e^{3} + 9e$ |
| 31 | $[31, 31, w + 3]$ | $\phantom{-}e^{2} - 3$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $\phantom{-}2e^{3} - 20e$ |
| 37 | $[37, 37, w^{2} - 3]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{27}{2}e$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ | $-e^{3} + 9e$ |
| 47 | $[47, 47, w^{3} - 5w - 3]$ | $-2e^{3} + 22e$ |
| 53 | $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ | $\phantom{-}\frac{5}{2}e^{3} - \frac{45}{2}e$ |
| 61 | $[61, 61, w^{3} - w^{2} - 5w + 3]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}$ |
| 83 | $[83, 83, w^{3} + w^{2} - 6w - 7]$ | $\phantom{-}2e$ |
| 83 | $[83, 83, -w^{3} + 5w + 1]$ | $-2e^{2} + 12$ |
| 83 | $[83, 83, 2w - 1]$ | $-3e^{3} + 29e$ |
| 83 | $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ | $\phantom{-}4$ |
| 89 | $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ | $-\frac{1}{2}e^{2} - \frac{3}{2}$ |
| 89 | $[89, 89, w^{3} - 5w + 5]$ | $-\frac{3}{2}e^{2} + \frac{15}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 1]$ | $1$ |