Base field 3.3.1940.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + x^{7} - 14x^{6} - 11x^{5} + 59x^{4} + 24x^{3} - 84x^{2} + 4x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - 7]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{1}{8}e^{6} - \frac{7}{4}e^{5} + \frac{11}{8}e^{4} + \frac{53}{8}e^{3} - 3e^{2} - \frac{19}{4}e - \frac{3}{2}$ |
| 5 | $[5, 5, -w - 3]$ | $-\frac{1}{4}e^{6} - \frac{1}{4}e^{5} + 3e^{4} + \frac{9}{4}e^{3} - \frac{35}{4}e^{2} - \frac{5}{2}e + \frac{9}{2}$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{1}{8}e^{6} - \frac{3}{2}e^{5} - \frac{13}{8}e^{4} + \frac{35}{8}e^{3} + \frac{19}{4}e^{2} - \frac{5}{4}e - 2$ |
| 17 | $[17, 17, -2w^{2} + 15]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{13}{4}e^{5} - \frac{1}{4}e^{4} + 12e^{3} + \frac{7}{4}e^{2} - 13e - \frac{3}{2}$ |
| 17 | $[17, 17, 3w + 1]$ | $\phantom{-}\frac{3}{8}e^{7} + \frac{3}{8}e^{6} - \frac{9}{2}e^{5} - \frac{31}{8}e^{4} + \frac{105}{8}e^{3} + \frac{29}{4}e^{2} - \frac{31}{4}e$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{3}{8}e^{6} - 2e^{5} + \frac{35}{8}e^{4} + \frac{79}{8}e^{3} - \frac{47}{4}e^{2} - \frac{49}{4}e + 3$ |
| 19 | $[19, 19, -2w^{2} + w + 15]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{3}{4}e^{6} - \frac{7}{2}e^{5} - \frac{33}{4}e^{4} + \frac{57}{4}e^{3} + 19e^{2} - \frac{39}{2}e - 1$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{3}{8}e^{7} + \frac{5}{8}e^{6} - \frac{17}{4}e^{5} - \frac{55}{8}e^{4} + \frac{95}{8}e^{3} + 16e^{2} - \frac{41}{4}e - \frac{9}{2}$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{11}{8}e^{6} - \frac{5}{4}e^{5} - \frac{125}{8}e^{4} + \frac{25}{8}e^{3} + \frac{83}{2}e^{2} - \frac{31}{4}e - \frac{33}{2}$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{1}{2}e^{7} - \frac{1}{2}e^{6} + 6e^{5} + \frac{11}{2}e^{4} - \frac{37}{2}e^{3} - 11e^{2} + 15e - 4$ |
| 47 | $[47, 47, 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{1}{2}e^{5} - 6e^{4} + \frac{13}{2}e^{3} + \frac{35}{2}e^{2} - 19e - 3$ |
| 53 | $[53, 53, -2w - 3]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{3}{8}e^{6} - \frac{5}{4}e^{5} - \frac{37}{8}e^{4} + \frac{17}{8}e^{3} + \frac{29}{2}e^{2} + \frac{9}{4}e - \frac{9}{2}$ |
| 59 | $[59, 59, w^{2} - w - 11]$ | $-\frac{1}{2}e^{6} + \frac{1}{2}e^{5} + 6e^{4} - \frac{13}{2}e^{3} - \frac{35}{2}e^{2} + 21e + 9$ |
| 71 | $[71, 71, w^{2} - 3]$ | $\phantom{-}\frac{1}{4}e^{7} + \frac{1}{4}e^{6} - 4e^{5} - \frac{9}{4}e^{4} + \frac{79}{4}e^{3} + \frac{5}{2}e^{2} - \frac{57}{2}e + 6$ |
| 73 | $[73, 73, 6w^{2} - 2w - 47]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{3}{8}e^{6} - \frac{5}{4}e^{5} - \frac{37}{8}e^{4} + \frac{9}{8}e^{3} + \frac{27}{2}e^{2} + \frac{17}{4}e - \frac{17}{2}$ |
| 83 | $[83, 83, w^{2} - 4w + 1]$ | $-\frac{1}{2}e^{7} - e^{6} + \frac{11}{2}e^{5} + \frac{23}{2}e^{4} - 13e^{3} - \frac{59}{2}e^{2} + 4e + 15$ |
| 83 | $[83, 83, 3w^{2} - 25]$ | $\phantom{-}e^{7} + e^{6} - 12e^{5} - 11e^{4} + 37e^{3} + 26e^{2} - 30e - 12$ |
| 83 | $[83, 83, w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - 6e^{5} + \frac{13}{2}e^{4} + \frac{35}{2}e^{3} - 21e^{2} - 7e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{2} - 7]$ | $-1$ |