Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23,23,w^{3} + w^{2} - 4w - 1]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - 13x^{3} + 8x^{2} + 16x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w + 2]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{13}{4}e^{2} + e + 3$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{11}{2}e^{2} + \frac{3}{2}e - 5$ |
| 13 | $[13, 13, w^{3} - 6w + 4]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + \frac{3}{2}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e$ |
| 17 | $[17, 17, w^{2} + w - 2]$ | $-\frac{1}{4}e^{4} + \frac{11}{4}e^{2} - \frac{5}{2}e$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 6e$ |
| 23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $-\frac{3}{4}e^{4} - \frac{1}{2}e^{3} + \frac{37}{4}e^{2} + e - 11$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -w^{2} + 3]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{15}{4}e^{2} - 6e - 5$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + \frac{7}{2}e - 2$ |
| 29 | $[29, 29, -w^{2} - 2w + 3]$ | $\phantom{-}\frac{3}{4}e^{4} + \frac{1}{2}e^{3} - \frac{39}{4}e^{2} - \frac{1}{2}e + 12$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{4}e^{2} + \frac{5}{2}e - 4$ |
| 43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $-e - 2$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{13}{2}e^{2} + \frac{5}{2}e - 13$ |
| 53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $-\frac{1}{4}e^{4} + \frac{1}{2}e^{3} + \frac{13}{4}e^{2} - \frac{11}{2}e + 2$ |
| 53 | $[53, 53, w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{15}{2}e^{2} + \frac{15}{2}e + 7$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $-\frac{3}{4}e^{4} - \frac{1}{2}e^{3} + \frac{37}{4}e^{2} - 2e - 13$ |
| 61 | $[61, 61, w^{3} - 7w + 3]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - \frac{37}{2}e^{2} + \frac{9}{2}e + 13$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{7}{4}e^{2} - 3e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,w^{3} + w^{2} - 4w - 1]$ | $-1$ |