Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[11,11,w^{2} - 3w - 7]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} - 64x^{10} + 1492x^{8} + 219x^{7} - 15257x^{6} - 7355x^{5} + 63200x^{4} + 64940x^{3} - 57224x^{2} - 99360x - 33984\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
8 | $[8, 2, 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w]$ | $...$ |
11 | $[11, 11, -w^{2} + 3w + 7]$ | $\phantom{-}1$ |
11 | $[11, 11, w^{2} - 2w - 8]$ | $...$ |
23 | $[23, 23, w^{2} - 2w - 7]$ | $...$ |
23 | $[23, 23, w^{2} - 3w - 8]$ | $...$ |
23 | $[23, 23, w - 1]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, w^{2} - 2w - 5]$ | $...$ |
29 | $[29, 29, w^{2} - 3w - 10]$ | $...$ |
29 | $[29, 29, w - 3]$ | $...$ |
31 | $[31, 31, w^{2} - 2w - 6]$ | $...$ |
31 | $[31, 31, -w^{2} + 3w + 9]$ | $...$ |
31 | $[31, 31, w - 2]$ | $...$ |
37 | $[37, 37, -w^{2} + 4w + 7]$ | $...$ |
43 | $[43, 43, 2w^{2} - 6w - 13]$ | $...$ |
43 | $[43, 43, 2w^{2} - 4w - 17]$ | $...$ |
43 | $[43, 43, w^{2} - 2w - 12]$ | $...$ |
47 | $[47, 47, w^{2} - 4w - 4]$ | $...$ |
47 | $[47, 47, w^{2} - w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,w^{2} - 3w - 7]$ | $-1$ |