Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23,23,-w^{3} + 2w^{2} + 4w - 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 9x^{4} + 2x^{3} + 17x^{2} - 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + \frac{1}{2}e^{2} + 8e - \frac{3}{2}$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-1$ |
| 13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $-\frac{1}{2}e^{4} - e^{3} + 4e^{2} + 5e - \frac{9}{2}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $-e^{5} + \frac{17}{2}e^{3} - \frac{5}{2}e^{2} - \frac{29}{2}e + \frac{7}{2}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{3} + e^{2} - 4e - 3$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}e^{5} + \frac{1}{2}e^{4} - \frac{19}{2}e^{3} - \frac{3}{2}e^{2} + \frac{35}{2}e - 5$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}1$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 4e^{3} + 2e^{2} - \frac{11}{2}e + \frac{1}{2}$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $\phantom{-}\frac{3}{2}e^{5} + 2e^{4} - 11e^{3} - 10e^{2} + \frac{31}{2}e + 3$ |
| 53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $-2e^{5} - e^{4} + 19e^{3} + 3e^{2} - 41e + 4$ |
| 53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $-\frac{3}{2}e^{5} - \frac{3}{2}e^{4} + 12e^{3} + 5e^{2} - \frac{37}{2}e + \frac{13}{2}$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - 4e^{3} - e^{2} + \frac{9}{2}e + 5$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}e^{5} + \frac{3}{2}e^{4} - \frac{17}{2}e^{3} - \frac{21}{2}e^{2} + \frac{25}{2}e + 9$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} + \frac{1}{2}e^{2} - 19e + \frac{1}{2}$ |
| 79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $-\frac{3}{2}e^{5} - \frac{5}{2}e^{4} + 11e^{3} + 14e^{2} - \frac{31}{2}e - \frac{25}{2}$ |
| 79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}2e^{5} + e^{4} - 16e^{3} - 4e^{2} + 22e - 3$ |
| 101 | $[101, 101, w^{3} - 6w]$ | $-\frac{5}{2}e^{4} - 2e^{3} + 17e^{2} + 7e - \frac{37}{2}$ |
| 101 | $[101, 101, w^{2} - 2w - 4]$ | $-4e^{5} - e^{4} + \frac{71}{2}e^{3} + \frac{3}{2}e^{2} - \frac{133}{2}e + \frac{19}{2}$ |
| 103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - \frac{9}{2}e^{2} - \frac{9}{2}e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23,23,-w^{3} + 2w^{2} + 4w - 4]$ | $-1$ |