Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $66$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 6$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{1}{2}e^{3} + 5e$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $-\frac{1}{2}e^{3} + 3e$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $-2e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{1}{4}e^{3} + \frac{3}{2}e$ |
| 23 | $[23, 23, -w + 4]$ | $-1$ |
| 27 | $[27, 3, 3]$ | $-\frac{1}{2}e^{2} + 4$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-\frac{1}{2}e^{2} + 4$ |
| 41 | $[41, 41, w + 4]$ | $-e^{2} + 6$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-e^{3} + 10e$ |
| 41 | $[41, 41, -2w - 5]$ | $\phantom{-}\frac{5}{4}e^{3} - \frac{23}{2}e$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{15}{2}e$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}e^{3} - 8e$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $-e^{3} + 14e$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $\phantom{-}\frac{3}{2}e^{3} - 13e$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w + 4]$ | $1$ |