Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, -3]$ |
| 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:
| \(x^{6} - 24x^{4} + 135x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{18}e^{4} + \frac{11}{18}e^{2} - \frac{5}{9}$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{17}{9}e^{2} + \frac{16}{9}$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{1}{18}e^{5} + \frac{29}{18}e^{3} - \frac{104}{9}e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{1}{18}e^{5} + \frac{17}{18}e^{3} - \frac{26}{9}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{23}{6}e^{3} + \frac{59}{3}e$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-\frac{1}{18}e^{4} + \frac{17}{18}e^{2} - \frac{44}{9}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{5}{18}e^{5} + \frac{127}{18}e^{3} - \frac{385}{9}e$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $\phantom{-}\frac{2}{9}e^{5} - \frac{52}{9}e^{3} + \frac{320}{9}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{9}e^{5} + \frac{20}{9}e^{3} - \frac{82}{9}e$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{2}{9}e^{5} - \frac{43}{9}e^{3} + \frac{203}{9}e$ |
| 27 | $[27, 3, -3]$ | $-1$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $-\frac{1}{9}e^{4} + \frac{20}{9}e^{2} - \frac{64}{9}$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{2}{9}e^{4} - \frac{25}{9}e^{2} - \frac{22}{9}$ |
| 41 | $[41, 41, -w - 4]$ | $-\frac{7}{18}e^{4} + \frac{107}{18}e^{2} - \frac{104}{9}$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{6}e^{4} - \frac{5}{2}e^{2} - \frac{8}{3}$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $-\frac{2}{9}e^{5} + \frac{52}{9}e^{3} - \frac{338}{9}e$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{20}{9}e^{2} - \frac{26}{9}$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{1}{9}e^{5} + \frac{20}{9}e^{3} - \frac{73}{9}e$ |
| 67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{5}{9}e^{5} - \frac{124}{9}e^{3} + \frac{722}{9}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, -3]$ | $1$ |