Base field 4.4.10304.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 5x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + w - 3]$ | $-2e^{3} + 8e$ |
| 23 | $[23, 23, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ | $-2e^{2} + 4$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{9}{2}w + 1]$ | $-e^{3} + 5e$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{5}{2}w - 1]$ | $-e^{3} + 5e$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 1]$ | $-2e$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w + 1]$ | $-2e$ |
| 41 | $[41, 41, \frac{3}{2}w^{3} - w^{2} - \frac{21}{2}w - 5]$ | $\phantom{-}3e^{3} - 13e$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 7]$ | $\phantom{-}3e^{3} - 13e$ |
| 47 | $[47, 47, -w^{2} - w + 5]$ | $\phantom{-}2e^{2} - 8$ |
| 47 | $[47, 47, -w^{3} + \frac{1}{2}w^{2} + \frac{13}{2}w + 5]$ | $\phantom{-}2e^{2} - 8$ |
| 49 | $[49, 7, \frac{1}{2}w^{2} - \frac{1}{2}w - 5]$ | $\phantom{-}12$ |
| 73 | $[73, 73, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $-5e^{3} + 19e$ |
| 73 | $[73, 73, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 1]$ | $-5e^{3} + 19e$ |
| 79 | $[79, 79, w^{2} - 3w + 1]$ | $\phantom{-}4e^{3} - 22e$ |
| 79 | $[79, 79, w^{2} + w - 1]$ | $\phantom{-}4e^{3} - 22e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}6e^{2} - 10$ |
| 89 | $[89, 89, -\frac{1}{2}w^{3} + 3w^{2} + \frac{7}{2}w - 11]$ | $\phantom{-}5e^{3} - 15e$ |
| 89 | $[89, 89, \frac{1}{2}w^{3} - \frac{5}{2}w - 3]$ | $\phantom{-}2e^{2} - 4$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).