Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ |
Dimension: | $13$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{13} + 3x^{12} - 29x^{11} - 77x^{10} + 298x^{9} + 629x^{8} - 1450x^{7} - 2151x^{6} + 3247x^{5} + 3482x^{4} - 3006x^{3} - 2511x^{2} + 756x + 441\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $...$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $...$ |
7 | $[7, 7, -w^{2} + 2]$ | $...$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $...$ |
16 | $[16, 2, 2]$ | $...$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}1$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $...$ |
25 | $[25, 5, w^{2} - w - 3]$ | $...$ |
37 | $[37, 37, 2w - 1]$ | $...$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $...$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $...$ |
59 | $[59, 59, 2w - 5]$ | $...$ |
59 | $[59, 59, -2w - 3]$ | $...$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $...$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $...$ |
83 | $[83, 83, -w^{3} + 7w]$ | $...$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $...$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $...$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-1$ |