Base field 4.4.12400.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9,3,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{9}{2}]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 5x^{2} - 8x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ | $\phantom{-}e^{3} + e^{2} - 4e - 1$ |
| 5 | $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ | $-e^{3} - e^{2} + 5e + 3$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ | $-e^{3} - e^{2} + 6e + 4$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ | $-1$ |
| 19 | $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ | $\phantom{-}e^{2} + e$ |
| 19 | $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ | $-2e^{2} - 2e + 6$ |
| 29 | $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ | $-2e^{3} - 4e^{2} + 10e + 8$ |
| 29 | $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ | $-2e^{3} - e^{2} + 10e + 5$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $\phantom{-}e^{3} + e^{2} - 8e - 2$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ | $\phantom{-}3e^{3} + 2e^{2} - 16e - 10$ |
| 59 | $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ | $-2e^{3} + 14e + 3$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ | $\phantom{-}e^{2} - e + 2$ |
| 61 | $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}e^{2} + 5e - 4$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ | $-e^{3} + 3e - 5$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ | $\phantom{-}e^{3} + 5e^{2} - 3e - 15$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ | $\phantom{-}e^{3} - e^{2} - 7e - 1$ |
| 79 | $[79, 79, -2w^{2} + w + 10]$ | $\phantom{-}2e^{2} - 3e - 16$ |
| 79 | $[79, 79, 2w^{2} + w - 10]$ | $-e^{3} - 2e^{2} + 4$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ | $-2e^{2} - e + 13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9,3,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{9}{2}]$ | $1$ |