Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 5x^{2} - 12x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $\phantom{-}e + 1$ |
| 5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $\phantom{-}e + 1$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $-e^{3} - 2e^{2} + 4e + 3$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $-e^{3} - 2e^{2} + 4e + 3$ |
| 31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $-e^{3} - e^{2} + 4e - 2$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $-e^{3} - e^{2} + 4e - 2$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $-e^{3} - e^{2} + 5e + 3$ |
| 41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $-e^{3} - e^{2} + 6e - 2$ |
| 41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-e^{3} - e^{2} + 6e - 2$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $-e^{3} - e^{2} + 5e + 3$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $\phantom{-}2e^{2} + 4e - 8$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}2e^{2} + 4e - 8$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $\phantom{-}e^{3} - e^{2} - 7e + 7$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $\phantom{-}e^{3} - e^{2} - 7e + 7$ |
| 81 | $[81, 3, -3]$ | $-3e^{2} - 5e + 18$ |
| 89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $\phantom{-}3e^{2} + 5e - 10$ |
| 89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $\phantom{-}e^{3} - 7e$ |
| 89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $\phantom{-}e^{3} - 7e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).