Base field 4.4.13968.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 14x^{6} + 57x^{4} - 56x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{55}{4}e^{3} + \frac{21}{2}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $-1$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ | $-\frac{1}{2}e^{6} + \frac{11}{2}e^{4} - 15e^{2} + 6$ |
| 13 | $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{6} - 5e^{4} + \frac{23}{2}e^{2} - 1$ |
| 23 | $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + e$ |
| 23 | $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ | $-e^{3} + 7e$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 4e^{4} + \frac{9}{2}e^{2} + 5$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ | $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 22e^{2} + 12$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ | $\phantom{-}\frac{1}{2}e^{7} - 7e^{5} + \frac{59}{2}e^{3} - 39e$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ | $\phantom{-}e^{7} - 15e^{5} + 62e^{3} - 46e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ | $-e^{4} + 5e^{2} + 8$ |
| 61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + \frac{37}{2}e^{2} - 3$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ | $-\frac{1}{2}e^{6} + \frac{9}{2}e^{4} - 8e^{2} + 4$ |
| 61 | $[61, 61, w^{3} - w^{2} - 8w + 1]$ | $-e^{4} + 9e^{2} - 6$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ | $-e^{5} + 11e^{3} - 26e$ |
| 71 | $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ | $-e^{7} + 12e^{5} - 39e^{3} + 24e$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ | $\phantom{-}e^{7} - 14e^{5} + 56e^{3} - 47e$ |
| 83 | $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ | $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 24e^{3} + 16e$ |
| 97 | $[97, 97, 2w - 1]$ | $-\frac{3}{2}e^{4} + \frac{21}{2}e^{2} - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $1$ |