Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 23x^{2} - 12x + 88\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 2]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{13}{6}e + \frac{10}{3}$ |
| 4 | $[4, 2, -w^{2} + 3w + 3]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} + 2w + 7]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}e - 2$ |
| 13 | $[13, 13, -w + 3]$ | $-\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{19}{6}e - \frac{4}{3}$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{16}{3}e + \frac{14}{3}$ |
| 17 | $[17, 17, -w^{2} - 2w + 1]$ | $-\frac{1}{6}e^{3} + \frac{1}{3}e^{2} + \frac{7}{6}e - \frac{4}{3}$ |
| 23 | $[23, 23, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{5}{3}e^{2} - \frac{10}{3}e + \frac{50}{3}$ |
| 31 | $[31, 31, 2w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{11}{2}e + 18$ |
| 31 | $[31, 31, -2w^{2} + 3w + 15]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{13}{3}e + \frac{20}{3}$ |
| 31 | $[31, 31, 3w + 7]$ | $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{13}{6}e + \frac{22}{3}$ |
| 37 | $[37, 37, 3w^{2} - 4w - 27]$ | $\phantom{-}\frac{5}{6}e^{3} - \frac{8}{3}e^{2} - \frac{71}{6}e + \frac{56}{3}$ |
| 41 | $[41, 41, -2w^{2} + 7w + 1]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{19}{3}e + \frac{10}{3}$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{2}{3}e^{3} + \frac{7}{3}e^{2} + \frac{23}{3}e - \frac{64}{3}$ |
| 61 | $[61, 61, 4w^{2} - 12w - 11]$ | $-\frac{2}{3}e^{3} + \frac{4}{3}e^{2} + \frac{29}{3}e - \frac{34}{3}$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{11}{2}e + 22$ |
| 97 | $[97, 97, 3w + 5]$ | $-3e + 2$ |
| 101 | $[101, 101, 2w^{2} - 6w - 7]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{22}{3}e - \frac{14}{3}$ |
| 103 | $[103, 103, 2w^{2} - 3w - 19]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{10}{3}e - \frac{22}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 2]$ | $1$ |
| $4$ | $[4, 2, -w^{2} + 3w + 3]$ | $-1$ |