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: | $[17, 17, -w^{2} - w + 5]$ |
Dimension: | $28$ |
CM: | no |
Base change: | no |
Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{28} + 2x^{27} - 40x^{26} - 80x^{25} + 698x^{24} + 1402x^{23} - 6978x^{22} - 14165x^{21} + 44110x^{20} + 91345x^{19} - 183443x^{18} - 393212x^{17} + 505268x^{16} + 1148457x^{15} - 900406x^{14} - 2269009x^{13} + 964923x^{12} + 2971469x^{11} - 486417x^{10} - 2476413x^{9} - 71299x^{8} + 1221981x^{7} + 210259x^{6} - 311690x^{5} - 88497x^{4} + 29044x^{3} + 11368x^{2} + 280x - 84\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 2]$ | $...$ |
9 | $[9, 3, w^{2} + w - 7]$ | $...$ |
11 | $[11, 11, w]$ | $...$ |
11 | $[11, 11, -2w + 3]$ | $...$ |
11 | $[11, 11, -w^{2} + 3w - 1]$ | $...$ |
17 | $[17, 17, w + 2]$ | $...$ |
17 | $[17, 17, -2w + 5]$ | $...$ |
17 | $[17, 17, -w^{2} - w + 5]$ | $-1$ |
23 | $[23, 23, w - 4]$ | $...$ |
29 | $[29, 29, w^{2} - 6]$ | $...$ |
31 | $[31, 31, w^{2} - w - 1]$ | $...$ |
37 | $[37, 37, -w^{2} - 2w + 6]$ | $...$ |
43 | $[43, 43, w^{2} - 3w + 3]$ | $...$ |
47 | $[47, 47, 3w^{2} - 28]$ | $...$ |
53 | $[53, 53, w^{2} - w - 3]$ | $...$ |
61 | $[61, 61, -5w + 6]$ | $...$ |
71 | $[71, 71, w^{2} - w - 7]$ | $...$ |
83 | $[83, 83, -2w^{2} - w + 14]$ | $...$ |
89 | $[89, 89, w^{2} + 3w - 3]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} - w + 5]$ | $1$ |