Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^3 - x^2 - 9 x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[2, 2, w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 - 2 x^5 - 16 x^4 + 26 x^3 + 60 x^2 - 66 x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 2]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^2 + 3 w + 3]$ | $-\frac{2}{9} e^5 + \frac{1}{3} e^4 + \frac{29}{9} e^3 - \frac{11}{3} e^2 - \frac{32}{3} e + \frac{19}{3}$ |
| 9 | $[9, 3, -w^2 + 2 w + 7]$ | $\phantom{-}\frac{1}{6} e^5 - \frac{8}{3} e^3 + 10 e - 3$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{18} e^5 - \frac{1}{3} e^4 - \frac{14}{9} e^3 + \frac{11}{3} e^2 + \frac{32}{3} e - \frac{13}{3}$ |
| 13 | $[13, 13, -w + 3]$ | $-\frac{1}{18} e^5 + \frac{1}{3} e^4 + \frac{5}{9} e^3 - \frac{11}{3} e^2 - \frac{5}{3} e + \frac{19}{3}$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}\frac{1}{18} e^5 - \frac{1}{3} e^4 - \frac{14}{9} e^3 + \frac{11}{3} e^2 + \frac{32}{3} e - \frac{13}{3}$ |
| 17 | $[17, 17, -w^2 - 2 w + 1]$ | $\phantom{-}\frac{1}{6} e^5 - \frac{8}{3} e^3 + e^2 + 9 e - 7$ |
| 23 | $[23, 23, w^2 - 2 w - 5]$ | $\phantom{-}\frac{1}{3} e^5 - \frac{16}{3} e^3 + e^2 + 18 e - 10$ |
| 31 | $[31, 31, 2 w + 3]$ | $\phantom{-}\frac{2}{9} e^5 - \frac{1}{3} e^4 - \frac{38}{9} e^3 + \frac{14}{3} e^2 + \frac{59}{3} e - \frac{34}{3}$ |
| 31 | $[31, 31, -2 w^2 + 3 w + 15]$ | $-\frac{2}{3} e^5 + e^4 + \frac{32}{3} e^3 - 12 e^2 - 40 e + 20$ |
| 31 | $[31, 31, 3 w + 7]$ | $-\frac{2}{9} e^5 + \frac{1}{3} e^4 + \frac{38}{9} e^3 - \frac{14}{3} e^2 - \frac{53}{3} e + \frac{40}{3}$ |
| 37 | $[37, 37, 3 w^2 - 4 w - 27]$ | $\phantom{-}\frac{2}{9} e^5 - \frac{1}{3} e^4 - \frac{29}{9} e^3 + \frac{8}{3} e^2 + \frac{29}{3} e + \frac{8}{3}$ |
| 41 | $[41, 41, -2 w^2 + 7 w + 1]$ | $\phantom{-}\frac{1}{2} e^5 - 8 e^3 + e^2 + 30 e - 13$ |
| 59 | $[59, 59, w^2 - 3]$ | $-\frac{1}{3} e^5 + e^4 + \frac{16}{3} e^3 - 10 e^2 - 24 e + 6$ |
| 61 | $[61, 61, 4 w^2 - 12 w - 11]$ | $-\frac{11}{18} e^5 + \frac{2}{3} e^4 + \frac{82}{9} e^3 - \frac{19}{3} e^2 - \frac{94}{3} e + \frac{23}{3}$ |
| 71 | $[71, 71, w^2 - 2 w - 11]$ | $-\frac{1}{3} e^5 + e^4 + \frac{19}{3} e^3 - 12 e^2 - 31 e + 14$ |
| 97 | $[97, 97, 3 w + 5]$ | $\phantom{-}\frac{5}{18} e^5 - \frac{2}{3} e^4 - \frac{52}{9} e^3 + \frac{25}{3} e^2 + \frac{88}{3} e - \frac{41}{3}$ |
| 101 | $[101, 101, 2 w^2 - 6 w - 7]$ | $\phantom{-}\frac{1}{2} e^5 - e^4 - 8 e^3 + 11 e^2 + 30 e - 19$ |
| 103 | $[103, 103, 2 w^2 - 3 w - 19]$ | $-\frac{4}{9} e^5 + \frac{2}{3} e^4 + \frac{76}{9} e^3 - \frac{25}{3} e^2 - \frac{118}{3} e + \frac{38}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 2]$ | $-1$ |