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: | $[23, 23, -w^{2} - w + 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $70$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 5x^{4} - 10x^{3} + 61x^{2} + 24x - 180\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{18}e^{4} - \frac{1}{18}e^{3} + \frac{11}{9}e^{2} + \frac{17}{18}e - \frac{11}{3}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{8}{9}e^{3} + \frac{5}{9}e^{2} + \frac{55}{9}e - \frac{17}{3}$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{2}{9}e^{4} - \frac{7}{9}e^{3} - \frac{17}{9}e^{2} + \frac{47}{9}e + \frac{14}{3}$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{1}{18}e^{4} + \frac{1}{18}e^{3} - \frac{11}{9}e^{2} - \frac{35}{18}e + \frac{17}{3}$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{16}{3}e^{2} - \frac{13}{3}e - 22$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $-\frac{1}{18}e^{4} + \frac{17}{18}e^{3} - \frac{25}{9}e^{2} - \frac{91}{18}e + \frac{67}{3}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w + 4]$ | $\phantom{-}\frac{5}{18}e^{4} - \frac{13}{18}e^{3} - \frac{28}{9}e^{2} + \frac{95}{18}e + \frac{13}{3}$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{8}{9}e^{3} + \frac{5}{9}e^{2} + \frac{37}{9}e - \frac{14}{3}$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $\phantom{-}e^{2} - 2e - 10$ |
| 31 | $[31, 31, w^{2} - 10]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 9e^{2} - \frac{9}{2}e - 33$ |
| 41 | $[41, 41, w + 4]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{8}{9}e^{3} + \frac{5}{9}e^{2} + \frac{64}{9}e - \frac{14}{3}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{2}{9}e^{4} - \frac{16}{9}e^{3} + \frac{28}{9}e^{2} + \frac{92}{9}e - \frac{76}{3}$ |
| 41 | $[41, 41, -2w - 5]$ | $\phantom{-}\frac{13}{18}e^{4} - \frac{41}{18}e^{3} - \frac{62}{9}e^{2} + \frac{265}{18}e + \frac{59}{3}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 9e^{2} - \frac{5}{2}e - 41$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}\frac{1}{18}e^{4} - \frac{17}{18}e^{3} + \frac{16}{9}e^{2} + \frac{127}{18}e - \frac{31}{3}$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $\phantom{-}\frac{7}{18}e^{4} - \frac{29}{18}e^{3} - \frac{23}{9}e^{2} + \frac{187}{18}e + \frac{5}{3}$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $-\frac{1}{9}e^{4} - \frac{10}{9}e^{3} + \frac{40}{9}e^{2} + \frac{89}{9}e - \frac{58}{3}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 4e^{2} + \frac{15}{2}e + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} - w + 3]$ | $-1$ |