Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{2} + 3]$ |
Dimension: | $13$ |
CM: | no |
Base change: | no |
Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{13} - 40x^{11} - 7x^{10} + 584x^{9} + 274x^{8} - 3874x^{7} - 2989x^{6} + 11027x^{5} + 11035x^{4} - 9108x^{3} - 9394x^{2} + 691x + 133\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $...$ |
5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2]$ | $...$ |
13 | $[13, 13, -w^{2} + 3]$ | $-1$ |
13 | $[13, 13, w^{2} - w - 4]$ | $...$ |
16 | $[16, 2, 2]$ | $...$ |
19 | $[19, 19, -w^{2} + w + 1]$ | $...$ |
23 | $[23, 23, -w^{3} + 4w + 2]$ | $...$ |
25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $...$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $...$ |
29 | $[29, 29, -w + 3]$ | $...$ |
31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $...$ |
37 | $[37, 37, w^{3} - 4w - 1]$ | $...$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $...$ |
53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $...$ |
59 | $[59, 59, w^{2} + w - 4]$ | $...$ |
61 | $[61, 61, -2w^{2} + w + 8]$ | $...$ |
73 | $[73, 73, -w^{3} + 5w - 1]$ | $...$ |
79 | $[79, 79, 2w^{2} + w - 6]$ | $...$ |
79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{2} + 3]$ | $1$ |