Base field 4.4.7168.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, -w^{3} - w^{2} + 3w + 4]$ |
| Dimension: | $8$ |
| 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:
| \(x^{8} - 13x^{6} + 51x^{4} - 63x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{21}{4}e^{3} - e$ |
| 9 | $[9, 3, w^{2} + w - 1]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 8e$ |
| 9 | $[9, 3, w^{2} - w - 1]$ | $-\frac{1}{4}e^{7} + 3e^{5} - \frac{39}{4}e^{3} + 8e$ |
| 17 | $[17, 17, -w^{3} + 3w - 1]$ | $\phantom{-}e^{3} - 5e$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + \frac{39}{2}e^{3} - 14e$ |
| 23 | $[23, 23, -w^{3} - w^{2} + 3w + 4]$ | $-1$ |
| 23 | $[23, 23, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{25}{4}e^{2} + 2$ |
| 41 | $[41, 41, w^{3} - w^{2} - 2w + 3]$ | $-\frac{1}{4}e^{6} + 2e^{4} - \frac{11}{4}e^{2}$ |
| 41 | $[41, 41, -w^{3} - w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{5}{2}e^{2} + 2$ |
| 49 | $[49, 7, w^{2} - 6]$ | $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{57}{4}e^{2} + 12$ |
| 71 | $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ | $-\frac{3}{4}e^{7} + \frac{17}{2}e^{5} - \frac{111}{4}e^{3} + 28e$ |
| 71 | $[71, 71, -2w^{2} - 2w + 1]$ | $\phantom{-}e^{7} - \frac{25}{2}e^{5} + \frac{91}{2}e^{3} - 46e$ |
| 73 | $[73, 73, w^{2} - 2w - 2]$ | $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{25}{4}e^{3} + 2e$ |
| 73 | $[73, 73, w^{2} + 2w - 2]$ | $-\frac{1}{4}e^{7} + \frac{3}{2}e^{5} + \frac{15}{4}e^{3} - 21e$ |
| 79 | $[79, 79, w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}e^{7} - 11e^{5} + 31e^{3} - 21e$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 5w + 2]$ | $-\frac{1}{4}e^{7} + 3e^{5} - \frac{39}{4}e^{3} + 8e$ |
| 89 | $[89, 89, 2w - 1]$ | $-\frac{1}{4}e^{7} + 3e^{5} - \frac{43}{4}e^{3} + 11e$ |
| 89 | $[89, 89, -2w - 1]$ | $-\frac{1}{2}e^{7} + \frac{15}{2}e^{5} - 36e^{3} + 49e$ |
| 97 | $[97, 97, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}e^{3} - e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w^{3}-w^{2}+3w+4]$ | $1$ |