Base field 5.5.176281.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ |
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:
\(x^{12} - 13x^{11} + 49x^{10} + 29x^{9} - 524x^{8} + 554x^{7} + 1774x^{6} - 2882x^{5} - 2239x^{4} + 4436x^{3} + 636x^{2} - 1520x + 144\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - w - 2]$ | $...$ |
7 | $[7, 7, -w^{2} + 2]$ | $...$ |
11 | $[11, 11, -w^{2} + 3]$ | $...$ |
13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}1$ |
23 | $[23, 23, -w^{4} + 5w^{2} + w - 4]$ | $...$ |
31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $...$ |
32 | $[32, 2, 2]$ | $...$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $...$ |
41 | $[41, 41, w^{4} - w^{3} - 3w^{2} + w + 1]$ | $...$ |
47 | $[47, 47, -w^{3} + w^{2} + 4w]$ | $...$ |
61 | $[61, 61, -w^{4} + 6w^{2} + w - 4]$ | $...$ |
67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 4w - 3]$ | $...$ |
71 | $[71, 71, w^{4} - 6w^{2} + 7]$ | $...$ |
73 | $[73, 73, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $...$ |
83 | $[83, 83, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $...$ |
83 | $[83, 83, -w^{4} + 5w^{2} + 2w - 4]$ | $...$ |
83 | $[83, 83, w^{4} - 5w^{2} + 2]$ | $...$ |
89 | $[89, 89, -2w^{4} + 2w^{3} + 9w^{2} - 6w - 4]$ | $...$ |
101 | $[101, 101, -2w^{4} + 2w^{3} + 8w^{2} - 3w - 3]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-1$ |