Base field 3.3.1940.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[10, 10, -3w^{2} + w + 24]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 9x^{3} - 32x^{2} - 16x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $-1$ |
| 3 | $[3, 3, w^{2} - 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 5 | $[5, 5, -w - 3]$ | $-\frac{2}{3}e^{4} - \frac{5}{3}e^{3} + \frac{19}{3}e^{2} + \frac{53}{3}e + \frac{13}{3}$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $\phantom{-}e^{3} - 10e - 6$ |
| 17 | $[17, 17, -2w^{2} + 15]$ | $-\frac{1}{3}e^{4} + \frac{2}{3}e^{3} + \frac{8}{3}e^{2} - \frac{14}{3}e + \frac{8}{3}$ |
| 17 | $[17, 17, 3w + 1]$ | $-\frac{2}{3}e^{4} - \frac{8}{3}e^{3} + \frac{19}{3}e^{2} + \frac{80}{3}e + \frac{25}{3}$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $-\frac{2}{3}e^{4} - \frac{5}{3}e^{3} + \frac{22}{3}e^{2} + \frac{56}{3}e + \frac{4}{3}$ |
| 19 | $[19, 19, -2w^{2} + w + 15]$ | $-\frac{1}{3}e^{4} - \frac{1}{3}e^{3} + \frac{8}{3}e^{2} + \frac{13}{3}e + \frac{5}{3}$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{1}{3}e^{3} - \frac{8}{3}e^{2} - \frac{13}{3}e - \frac{23}{3}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{10}{3}e^{3} - \frac{41}{3}e^{2} - \frac{103}{3}e - \frac{29}{3}$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{7}{3}e^{4} - \frac{13}{3}e^{3} + \frac{68}{3}e^{2} + \frac{145}{3}e + \frac{23}{3}$ |
| 47 | $[47, 47, 2w - 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{11}{3}e^{2} - \frac{46}{3}e + \frac{4}{3}$ |
| 53 | $[53, 53, -2w - 3]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{5}{3}e^{3} - \frac{19}{3}e^{2} - \frac{59}{3}e - \frac{25}{3}$ |
| 59 | $[59, 59, w^{2} - w - 11]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{4}{3}e^{3} - \frac{41}{3}e^{2} - \frac{46}{3}e + \frac{16}{3}$ |
| 71 | $[71, 71, w^{2} - 3]$ | $\phantom{-}e^{4} + 3e^{3} - 9e^{2} - 33e - 16$ |
| 73 | $[73, 73, 6w^{2} - 2w - 47]$ | $-e^{3} + 12e + 6$ |
| 83 | $[83, 83, w^{2} - 4w + 1]$ | $-\frac{7}{3}e^{4} - \frac{19}{3}e^{3} + \frac{71}{3}e^{2} + \frac{205}{3}e + \frac{50}{3}$ |
| 83 | $[83, 83, 3w^{2} - 25]$ | $\phantom{-}\frac{13}{3}e^{4} + \frac{25}{3}e^{3} - \frac{128}{3}e^{2} - \frac{283}{3}e - \frac{62}{3}$ |
| 83 | $[83, 83, w - 5]$ | $\phantom{-}\frac{8}{3}e^{4} + \frac{11}{3}e^{3} - \frac{82}{3}e^{2} - \frac{131}{3}e - \frac{1}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $1$ |
| $5$ | $[5, 5, w + 1]$ | $1$ |