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: | $[9, 9, w^{2} - 2w - 9]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 11x^{4} + 22x^{3} + 17x^{2} - 36x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{4}e^{4} - 3e^{3} + \frac{5}{2}e^{2} + \frac{23}{4}e - \frac{9}{4}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{2} + 2w + 7]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} - \frac{1}{2}e^{2} + 10e + \frac{7}{2}$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{1}{2}e^{4} - \frac{11}{2}e^{3} + \frac{11}{2}e^{2} + 9e - 5$ |
| 13 | $[13, 13, -w + 3]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + \frac{1}{2}$ |
| 13 | $[13, 13, -w + 1]$ | $-e^{5} + \frac{1}{2}e^{4} + \frac{23}{2}e^{3} - \frac{9}{2}e^{2} - \frac{41}{2}e + 2$ |
| 17 | $[17, 17, -w^{2} - 2w + 1]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{11}{2}e^{3} - \frac{11}{2}e^{2} - 8e + 8$ |
| 23 | $[23, 23, w^{2} - 2w - 5]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + 6e^{3} - 6e^{2} - \frac{27}{2}e + \frac{19}{2}$ |
| 31 | $[31, 31, 2w + 3]$ | $-\frac{1}{2}e^{4} + 4e^{2} + e - \frac{1}{2}$ |
| 31 | $[31, 31, -2w^{2} + 3w + 15]$ | $-\frac{3}{2}e^{5} + e^{4} + 17e^{3} - 9e^{2} - \frac{61}{2}e + 7$ |
| 31 | $[31, 31, 3w + 7]$ | $\phantom{-}e^{2} - 5$ |
| 37 | $[37, 37, 3w^{2} - 4w - 27]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + 5e^{3} - 5e^{2} - \frac{9}{2}e + \frac{13}{2}$ |
| 41 | $[41, 41, -2w^{2} + 7w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{2}e + 12$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + 7e^{3} + 6e^{2} - \frac{41}{2}e - \frac{15}{2}$ |
| 61 | $[61, 61, 4w^{2} - 12w - 11]$ | $\phantom{-}2e^{5} - \frac{1}{2}e^{4} - \frac{47}{2}e^{3} + \frac{11}{2}e^{2} + \frac{93}{2}e - 2$ |
| 71 | $[71, 71, w^{2} - 2w - 11]$ | $\phantom{-}e^{5} - \frac{1}{2}e^{4} - 11e^{3} + 3e^{2} + 17e + \frac{21}{2}$ |
| 97 | $[97, 97, 3w + 5]$ | $-\frac{3}{2}e^{5} + \frac{35}{2}e^{3} - \frac{1}{2}e^{2} - 36e + \frac{1}{2}$ |
| 101 | $[101, 101, 2w^{2} - 6w - 7]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - \frac{13}{2}e^{3} - \frac{15}{2}e^{2} + 16e + 17$ |
| 103 | $[103, 103, 2w^{2} - 3w - 19]$ | $-\frac{5}{2}e^{5} + \frac{3}{2}e^{4} + 28e^{3} - 14e^{2} - \frac{95}{2}e + \frac{21}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |