Base field 3.3.1556.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[9, 9, -w^{2} + 10]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - 4x - 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}0$ |
9 | $[9, 3, w^{2} + w - 7]$ | $\phantom{-}e^{2} - 4$ |
11 | $[11, 11, w]$ | $-e^{2} + 6$ |
11 | $[11, 11, -2w + 3]$ | $\phantom{-}2e$ |
11 | $[11, 11, -w^{2} + 3w - 1]$ | $-2e$ |
17 | $[17, 17, w + 2]$ | $\phantom{-}e^{2} + 2e$ |
17 | $[17, 17, -2w + 5]$ | $\phantom{-}e^{2} - 6$ |
17 | $[17, 17, -w^{2} - w + 5]$ | $\phantom{-}e^{2} + 2e$ |
23 | $[23, 23, w - 4]$ | $-e^{2} + 6$ |
29 | $[29, 29, w^{2} - 6]$ | $\phantom{-}e^{2} + 2e - 6$ |
31 | $[31, 31, w^{2} - w - 1]$ | $-2e^{2} - 2e + 4$ |
37 | $[37, 37, -w^{2} - 2w + 6]$ | $-e^{2} + 10$ |
43 | $[43, 43, w^{2} - 3w + 3]$ | $-3e^{2} + 14$ |
47 | $[47, 47, 3w^{2} - 28]$ | $\phantom{-}2e^{2} + 2e$ |
53 | $[53, 53, w^{2} - w - 3]$ | $-e^{2} - 4e$ |
61 | $[61, 61, -5w + 6]$ | $\phantom{-}e^{2} - 4e - 4$ |
71 | $[71, 71, w^{2} - w - 7]$ | $\phantom{-}e^{2} + 6$ |
83 | $[83, 83, -2w^{2} - w + 14]$ | $\phantom{-}4e^{2} - 12$ |
89 | $[89, 89, w^{2} + 3w - 3]$ | $-3e^{2} + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 2]$ | $-1$ |