Base field 3.3.1300.1
Generator \(w\), with minimal polynomial \(x^{3} - 10x - 10\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[17, 17, -2w^{2} + 5w + 7]$ |
Dimension: | $16$ |
CM: | no |
Base change: | no |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} + 5x^{15} - 10x^{14} - 82x^{13} - 7x^{12} + 494x^{11} + 365x^{10} - 1401x^{9} - 1473x^{8} + 1950x^{7} + 2410x^{6} - 1248x^{5} - 1680x^{4} + 328x^{3} + 416x^{2} - 40x - 24\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{2} + 2w + 5]$ | $...$ |
7 | $[7, 7, w + 3]$ | $...$ |
11 | $[11, 11, -2w^{2} + 5w + 9]$ | $...$ |
13 | $[13, 13, -w^{2} + w + 7]$ | $...$ |
13 | $[13, 13, w - 3]$ | $...$ |
17 | $[17, 17, -w^{2} + 2w + 7]$ | $...$ |
17 | $[17, 17, -2w^{2} + 5w + 7]$ | $-1$ |
17 | $[17, 17, -w^{2} + 3w + 3]$ | $...$ |
19 | $[19, 19, -w + 1]$ | $...$ |
27 | $[27, 3, -3]$ | $...$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $...$ |
37 | $[37, 37, w^{2} - 7]$ | $...$ |
41 | $[41, 41, w^{2} - w - 11]$ | $...$ |
47 | $[47, 47, w^{2} - 3]$ | $...$ |
49 | $[49, 7, w^{2} - 3w - 1]$ | $...$ |
59 | $[59, 59, w^{2} - 4w + 1]$ | $...$ |
67 | $[67, 67, w^{2} - 3w - 7]$ | $...$ |
71 | $[71, 71, 4w + 9]$ | $...$ |
73 | $[73, 73, -4w^{2} + 8w + 23]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -2w^{2} + 5w + 7]$ | $1$ |