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: | $3$ |
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:
\(x^{3} - 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{2} - 7]$ | $-1$ |
5 | $[5, 5, w + 1]$ | $-e^{2} + e + 4$ |
5 | $[5, 5, -w - 3]$ | $-e + 1$ |
9 | $[9, 3, w^{2} - 2w - 1]$ | $-e - 3$ |
17 | $[17, 17, -2w^{2} + 15]$ | $-e^{2} + e$ |
17 | $[17, 17, 3w + 1]$ | $\phantom{-}e^{2} - 7$ |
17 | $[17, 17, -w^{2} + w + 5]$ | $\phantom{-}e^{2} - e - 4$ |
19 | $[19, 19, -2w^{2} + w + 15]$ | $\phantom{-}e^{2} - e - 2$ |
29 | $[29, 29, w^{2} - w - 1]$ | $-e^{2} - 1$ |
41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}2e + 4$ |
43 | $[43, 43, w^{2} + w - 3]$ | $-e - 9$ |
47 | $[47, 47, 2w - 1]$ | $-e^{2} - 4e + 5$ |
53 | $[53, 53, -2w - 3]$ | $-e^{2} + e - 4$ |
59 | $[59, 59, w^{2} - w - 11]$ | $\phantom{-}e^{2} + 2e - 3$ |
71 | $[71, 71, w^{2} - 3]$ | $\phantom{-}2e^{2} + e - 13$ |
73 | $[73, 73, 6w^{2} - 2w - 47]$ | $\phantom{-}2e^{2} - e + 3$ |
83 | $[83, 83, w^{2} - 4w + 1]$ | $\phantom{-}e^{2} + e$ |
83 | $[83, 83, 3w^{2} - 25]$ | $-4e^{2} - 2e + 14$ |
83 | $[83, 83, w - 5]$ | $\phantom{-}2e^{2} + 3e - 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w^{2} - 7]$ | $1$ |