Base field 4.4.7232.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23,23,w^{2} - w - 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 3x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 3]$ | $-e - 1$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}2e^{2} - 6$ |
| 17 | $[17, 17, -\frac{1}{2}w^{3} + 2w^{2} + \frac{1}{2}w - 2]$ | $-e^{2} + 1$ |
| 23 | $[23, 23, \frac{1}{2}w^{3} - 2w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}3e^{2} + 2e - 7$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 7]$ | $-3e^{2} - 6e + 5$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $\phantom{-}e^{2} - e - 2$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $\phantom{-}2e^{2} + 3e - 7$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w]$ | $\phantom{-}2e^{2} - 2e - 6$ |
| 47 | $[47, 47, \frac{3}{2}w^{3} - 4w^{2} - \frac{7}{2}w + 6]$ | $-2e^{2} + 3e + 5$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $-5e^{2} - 5e + 12$ |
| 49 | $[49, 7, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}e^{2} + 5e - 4$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - w^{2} - \frac{3}{2}w - 2]$ | $-4e^{2} - 4e + 6$ |
| 71 | $[71, 71, \frac{5}{2}w^{3} - 6w^{2} - \frac{17}{2}w + 12]$ | $-9e^{2} - 6e + 15$ |
| 71 | $[71, 71, 2w^{2} - 4w - 7]$ | $\phantom{-}2e - 6$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 5w - 3]$ | $-2e^{2} + 6e + 10$ |
| 73 | $[73, 73, 2w - 1]$ | $\phantom{-}e^{2} + 3e + 4$ |
| 79 | $[79, 79, \frac{3}{2}w^{3} - 4w^{2} - \frac{11}{2}w + 12]$ | $-e^{2} + 3e + 12$ |
| 79 | $[79, 79, -w^{2} - w - 1]$ | $-2e^{2} - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,w^{2} - w - 3]$ | $-1$ |