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: | $[2, 2, -w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 12x^{4} + 35x^{2} - 16\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w^{2} - 7]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e$ |
| 5 | $[5, 5, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 17 | $[17, 17, -2w^{2} + 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 2$ |
| 17 | $[17, 17, 3w + 1]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e$ |
| 19 | $[19, 19, -2w^{2} + w + 15]$ | $-\frac{1}{2}e^{5} + \frac{11}{2}e^{3} - 11e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{17}{2}e$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-e^{5} + \frac{21}{2}e^{3} - \frac{41}{2}e$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $\phantom{-}e^{3} - 5e$ |
| 47 | $[47, 47, 2w - 1]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 8$ |
| 53 | $[53, 53, -2w - 3]$ | $-\frac{1}{2}e^{5} + 6e^{3} - \frac{35}{2}e$ |
| 59 | $[59, 59, w^{2} - w - 11]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{29}{2}e^{2} + 20$ |
| 71 | $[71, 71, w^{2} - 3]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 10e$ |
| 73 | $[73, 73, 6w^{2} - 2w - 47]$ | $\phantom{-}\frac{1}{2}e^{5} - 7e^{3} + \frac{47}{2}e$ |
| 83 | $[83, 83, w^{2} - 4w + 1]$ | $-\frac{1}{2}e^{4} + \frac{13}{2}e^{2} - 4$ |
| 83 | $[83, 83, 3w^{2} - 25]$ | $-e^{4} + 8e^{2} - 12$ |
| 83 | $[83, 83, w - 5]$ | $-\frac{1}{2}e^{4} + \frac{15}{2}e^{2} - 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w]$ | $-1$ |