Base field 3.3.837.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[18, 6, w^{2} + w - 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 10x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2} - 2w - 1]$ | $-1$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
4 | $[4, 2, w^{2} + w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$ |
13 | $[13, 13, -2w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 1$ |
25 | $[25, 5, -w^{2} - 2w + 2]$ | $-e^{2} - e + 8$ |
31 | $[31, 31, -w^{2} + 2]$ | $-\frac{1}{2}e^{2} - \frac{3}{2}e + 4$ |
31 | $[31, 31, -2w + 1]$ | $\phantom{-}e^{2} + 3e - 8$ |
37 | $[37, 37, 2w + 3]$ | $-2e$ |
41 | $[41, 41, -w - 4]$ | $\phantom{-}6$ |
43 | $[43, 43, 2w^{2} - 2w - 7]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 1$ |
47 | $[47, 47, -2w^{2} - w + 8]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 10$ |
53 | $[53, 53, 3w^{2} - 6w - 2]$ | $-6$ |
53 | $[53, 53, -2w^{2} + 3w + 18]$ | $-e^{2} + e + 14$ |
53 | $[53, 53, 2w - 3]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e + 4$ |
59 | $[59, 59, 2w^{2} - 3w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{7}{2}e - 7$ |
61 | $[61, 61, w^{2} - 2w - 4]$ | $\phantom{-}e^{2} - e - 6$ |
71 | $[71, 71, 4w + 9]$ | $-\frac{1}{2}e^{2} - \frac{5}{2}e + 1$ |
73 | $[73, 73, 2w^{2} - 9]$ | $-e^{2} - e + 8$ |
79 | $[79, 79, w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{7}{2}e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{2} - 2w - 1]$ | $1$ |
$3$ | $[3, 3, w + 2]$ | $-1$ |