Base field 3.3.1436.1
Generator \(w\), with minimal polynomial \(x^{3} - 11x - 12\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[9, 3, -w^{2} + 3w + 5]$ |
Dimension: | $17$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{17} + 2x^{16} - 24x^{15} - 46x^{14} + 230x^{13} + 420x^{12} - 1123x^{11} - 1937x^{10} + 2948x^{9} + 4734x^{8} - 4010x^{7} - 5848x^{6} + 2433x^{5} + 3107x^{4} - 369x^{3} - 415x^{2} + 22x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $...$ |
3 | $[3, 3, w^{2} - w - 9]$ | $...$ |
9 | $[9, 3, -w^{2} + 3w + 5]$ | $\phantom{-}1$ |
11 | $[11, 11, -w^{2} + w + 11]$ | $...$ |
13 | $[13, 13, 2w^{2} - 4w - 13]$ | $...$ |
23 | $[23, 23, -w^{2} + w + 7]$ | $...$ |
29 | $[29, 29, -w^{2} - w + 1]$ | $...$ |
41 | $[41, 41, -2w^{2} + 2w + 19]$ | $...$ |
41 | $[41, 41, w^{2} - 3w - 7]$ | $...$ |
41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
47 | $[47, 47, 3w^{2} - 7w - 17]$ | $...$ |
53 | $[53, 53, -2w - 1]$ | $...$ |
61 | $[61, 61, -2w + 7]$ | $...$ |
67 | $[67, 67, 3w^{2} - 5w - 23]$ | $...$ |
67 | $[67, 67, 2w^{2} - 4w - 11]$ | $...$ |
67 | $[67, 67, 3w^{2} - 7w - 13]$ | $...$ |
79 | $[79, 79, w^{2} + w - 5]$ | $...$ |
89 | $[89, 89, 5w^{2} - 7w - 47]$ | $...$ |
97 | $[97, 97, 5w^{2} - 11w - 29]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, -w^{2} + 3w + 5]$ | $-1$ |