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: | $[3, 3, w^{2} - 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 2x^{2} - 12x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $-\frac{1}{3}e^{3} - e^{2} + \frac{2}{3}e + \frac{4}{3}$ |
3 | $[3, 3, w^{2} - 7]$ | $-1$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w - 3]$ | $-e^{2} - 2e + 2$ |
9 | $[9, 3, w^{2} - 2w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} + \frac{1}{3}e - \frac{10}{3}$ |
17 | $[17, 17, -2w^{2} + 15]$ | $-e^{2} - 4e + 2$ |
17 | $[17, 17, 3w + 1]$ | $-\frac{1}{3}e^{3} - 2e^{2} - \frac{1}{3}e + \frac{10}{3}$ |
17 | $[17, 17, -w^{2} + w + 5]$ | $-\frac{1}{3}e^{3} + \frac{11}{3}e - \frac{8}{3}$ |
19 | $[19, 19, -2w^{2} + w + 15]$ | $-2e - 4$ |
29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{4}{3}e^{3} + 4e^{2} - \frac{5}{3}e - \frac{10}{3}$ |
41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}\frac{2}{3}e^{3} + 4e^{2} + \frac{11}{3}e - \frac{32}{3}$ |
43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{4}{3}e^{3} - 4e^{2} + \frac{8}{3}e + \frac{16}{3}$ |
47 | $[47, 47, 2w - 1]$ | $-\frac{2}{3}e^{3} - 4e^{2} - \frac{8}{3}e + \frac{26}{3}$ |
53 | $[53, 53, -2w - 3]$ | $-\frac{2}{3}e^{3} - 4e^{2} + \frac{1}{3}e + \frac{26}{3}$ |
59 | $[59, 59, w^{2} - w - 11]$ | $\phantom{-}\frac{4}{3}e^{3} + 6e^{2} + \frac{4}{3}e - \frac{28}{3}$ |
71 | $[71, 71, w^{2} - 3]$ | $\phantom{-}\frac{2}{3}e^{3} + 4e^{2} + \frac{2}{3}e - \frac{8}{3}$ |
73 | $[73, 73, 6w^{2} - 2w - 47]$ | $\phantom{-}\frac{2}{3}e^{3} + 4e^{2} + \frac{11}{3}e - \frac{44}{3}$ |
83 | $[83, 83, w^{2} - 4w + 1]$ | $\phantom{-}2e^{2} - 16$ |
83 | $[83, 83, 3w^{2} - 25]$ | $\phantom{-}4e^{2} + 8e - 12$ |
83 | $[83, 83, w - 5]$ | $-2e^{3} - 6e^{2} + 8e + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{2} - 7]$ | $1$ |