Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ |
Dimension: | $20$ |
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:
\(x^{20} - 50x^{18} + 1023x^{16} - 11172x^{14} + 71111x^{12} - 269554x^{10} + 592673x^{8} - 688600x^{6} + 323688x^{4} - 6208x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - w - 5]$ | $...$ |
11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $...$ |
11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $...$ |
11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $...$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $...$ |
29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $...$ |
29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $...$ |
29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $...$ |
29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $...$ |
41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $-1$ |
41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $...$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $...$ |
41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $...$ |
79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $...$ |
79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $...$ |
79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $...$ |
79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $...$ |
81 | $[81, 3, -3]$ | $...$ |
109 | $[109, 109, w^{2} - w - 7]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $1$ |