Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[44, 22, -w^{2} + w + 6]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 4x^{2} + 11x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{2} - w - 5]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $\phantom{-}2e^{2} - 2e - 7$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $-e^{3} + e^{2} + 5e - 2$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 3$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $\phantom{-}e^{3} - 3e^{2} - e + 10$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $-e^{3} + 3e^{2} + 4e - 9$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $-2e + 1$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $-e^{3} + 6e + 5$ |
| 41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $-e^{2} - e + 2$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $-e^{3} - e^{2} + 6e + 12$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $-e^{3} + 2e^{2} + 5e - 8$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $-2e^{3} + e^{2} + 11e + 3$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $\phantom{-}3e^{2} - 3e - 10$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $\phantom{-}2e^{3} - e^{2} - 13e + 8$ |
| 79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $-e^{3} + 4e^{2} - e - 6$ |
| 79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $-2e^{3} + 2e^{2} + 13e - 7$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{3} - 5e^{2} - 2e + 17$ |
| 109 | $[109, 109, w^{2} - w - 7]$ | $\phantom{-}2e^{3} - 2e^{2} - 9e + 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $-1$ |
| $11$ | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $-1$ |