Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 4x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 9, w^{3} - 3w^{2} - 2w + 7]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 20x^{4} + 104x^{2} - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{24}e^{5} + \frac{5}{6}e^{3} - \frac{10}{3}e$ |
| 7 | $[7, 7, w - 2]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 10$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $-\frac{1}{4}e^{4} + 4e^{2} - 10$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $-\frac{1}{6}e^{5} + \frac{17}{6}e^{3} - \frac{28}{3}e$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{1}{12}e^{5} + \frac{7}{6}e^{3} - \frac{2}{3}e$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 6w + 2]$ | $-\frac{1}{12}e^{5} + \frac{5}{3}e^{3} - \frac{20}{3}e$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 16$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{1}{4}e^{5} + \frac{9}{2}e^{3} - 16e$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{1}{4}e^{4} + 2e^{2} + 8$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{7}{24}e^{5} - \frac{29}{6}e^{3} + \frac{43}{3}e$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{12}e^{5} - \frac{2}{3}e^{3} - \frac{10}{3}e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{3}{8}e^{5} + 6e^{3} - 16e$ |
| 73 | $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ | $\phantom{-}\frac{1}{24}e^{5} - \frac{5}{6}e^{3} + \frac{19}{3}e$ |
| 83 | $[83, 83, -w - 3]$ | $-\frac{3}{4}e^{4} + 12e^{2} - 34$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{11}{24}e^{5} - \frac{23}{3}e^{3} + \frac{65}{3}e$ |
| 89 | $[89, 89, 2w - 1]$ | $-\frac{5}{24}e^{5} + \frac{8}{3}e^{3} - \frac{11}{3}e$ |
| 101 | $[101, 101, w^{3} - 4w^{2} + w + 7]$ | $-\frac{3}{4}e^{4} + 12e^{2} - 36$ |
| 101 | $[101, 101, 2w^{2} - 3w - 3]$ | $-\frac{7}{24}e^{5} + \frac{13}{3}e^{3} - \frac{34}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $1$ |