Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 8 x^2 + 6 x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^6 - 12 x^4 + 4 x^3 + 39 x^2 - 18 x - 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3} w^3 - \frac{2}{3} w^2 - 2 w + 2]$ | $-\frac{1}{2} e^5 - e^4 + \frac{9}{2} e^3 + \frac{13}{2} e^2 - 10 e - 8$ |
| 9 | $[9, 3, w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 5 w]$ | $-\frac{1}{2} e^5 - e^4 + 4 e^3 + \frac{11}{2} e^2 - \frac{15}{2} e - \frac{11}{2}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{2} e^5 + \frac{5}{2} e^4 - 13 e^3 - 15 e^2 + 27 e + \frac{35}{2}$ |
| 17 | $[17, 17, \frac{1}{3} w^3 - \frac{2}{3} w^2 - 3 w + 5]$ | $\phantom{-}e^5 + \frac{3}{2} e^4 - 9 e^3 - \frac{21}{2} e^2 + \frac{37}{2} e + 15$ |
| 19 | $[19, 19, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 2 w - 5]$ | $-\frac{1}{2} e^5 - \frac{1}{2} e^4 + \frac{9}{2} e^3 + 3 e^2 - \frac{19}{2} e - 7$ |
| 23 | $[23, 23, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 3 w - 2]$ | $\phantom{-}e^5 + 2 e^4 - \frac{17}{2} e^3 - 13 e^2 + \frac{35}{2} e + \frac{29}{2}$ |
| 25 | $[25, 5, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 3 w]$ | $-e^5 - \frac{5}{2} e^4 + 8 e^3 + \frac{31}{2} e^2 - \frac{35}{2} e - 16$ |
| 25 | $[25, 5, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 5 w - 3]$ | $-\frac{1}{2} e^4 - e^3 + \frac{5}{2} e^2 + \frac{5}{2} e - 2$ |
| 29 | $[29, 29, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 4 w - 3]$ | $\phantom{-}\frac{1}{2} e^4 + \frac{3}{2} e^3 - \frac{5}{2} e^2 - 5 e - \frac{1}{2}$ |
| 29 | $[29, 29, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 2 w]$ | $\phantom{-}e^5 + 2 e^4 - \frac{19}{2} e^3 - 13 e^2 + \frac{45}{2} e + \frac{21}{2}$ |
| 37 | $[37, 37, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 2 w - 3]$ | $\phantom{-}\frac{1}{2} e^5 + \frac{1}{2} e^4 - \frac{7}{2} e^3 - 2 e^2 + \frac{5}{2} e + 3$ |
| 41 | $[41, 41, -\frac{2}{3} w^3 + \frac{1}{3} w^2 + 5 w - 4]$ | $\phantom{-}e^3 + 3 e^2 - 6 e - 8$ |
| 43 | $[43, 43, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 6 w]$ | $\phantom{-}\frac{1}{2} e^5 + \frac{1}{2} e^4 - \frac{5}{2} e^3 - e^2 - \frac{5}{2} e - 2$ |
| 47 | $[47, 47, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 4 w]$ | $-2 e^5 - 4 e^4 + \frac{33}{2} e^3 + 24 e^2 - \frac{67}{2} e - \frac{51}{2}$ |
| 59 | $[59, 59, \frac{1}{3} w^3 + \frac{1}{3} w^2 - 2 w - 4]$ | $\phantom{-}\frac{3}{2} e^5 + \frac{7}{2} e^4 - \frac{27}{2} e^3 - 24 e^2 + \frac{61}{2} e + 27$ |
| 59 | $[59, 59, \frac{4}{3} w^3 - \frac{5}{3} w^2 - 10 w + 9]$ | $-e^5 - \frac{1}{2} e^4 + 10 e^3 + \frac{3}{2} e^2 - \frac{45}{2} e - 2$ |
| 67 | $[67, 67, -\frac{1}{3} w^3 + \frac{2}{3} w^2 + 3 w]$ | $-\frac{5}{2} e^5 - \frac{7}{2} e^4 + 23 e^3 + 23 e^2 - 49 e - \frac{65}{2}$ |
| 71 | $[71, 71, \frac{2}{3} w^3 - \frac{1}{3} w^2 - 4 w + 1]$ | $-2 e^5 - \frac{5}{2} e^4 + 18 e^3 + \frac{29}{2} e^2 - \frac{73}{2} e - 17$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w + 1]$ | $-1$ |