Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[22, 22, -w^{3} + w^{2} + 3w - 2]$ |
Dimension: | $4$ |
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:
\(x^{4} - 6x^{3} - 6x^{2} + 45x + 27\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 2]$ | $\phantom{-}1$ |
3 | $[3, 3, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{3}e^{2} - e - 3$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-1$ |
13 | $[13, 13, w^{3} - 4w + 1]$ | $\phantom{-}\frac{1}{9}e^{3} - \frac{1}{3}e^{2} - \frac{5}{3}e$ |
13 | $[13, 13, -w^{3} + 4w + 1]$ | $-\frac{2}{9}e^{3} + \frac{2}{3}e^{2} + \frac{7}{3}e - 3$ |
25 | $[25, 5, -w^{2} - 2w + 1]$ | $-\frac{2}{9}e^{3} + \frac{1}{3}e^{2} + \frac{13}{3}e$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{2}{9}e^{3} + \frac{4}{3}e^{2} - \frac{2}{3}e - 9$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}\frac{4}{9}e^{3} - \frac{7}{3}e^{2} - \frac{5}{3}e + 6$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $-\frac{2}{9}e^{3} + e^{2} + \frac{4}{3}e - 6$ |
59 | $[59, 59, w^{2} - w - 5]$ | $-\frac{1}{3}e^{2} - e$ |
59 | $[59, 59, -w^{2} - w + 5]$ | $-e^{2} + e + 12$ |
61 | $[61, 61, -w^{3} + w^{2} + 4w - 7]$ | $\phantom{-}\frac{1}{9}e^{3} - e^{2} - \frac{2}{3}e + 3$ |
61 | $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ | $\phantom{-}\frac{1}{9}e^{3} + e^{2} - \frac{14}{3}e - 15$ |
73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}\frac{1}{3}e^{3} - 2e^{2} - 2e + 5$ |
73 | $[73, 73, 2w - 1]$ | $-\frac{2}{9}e^{3} + \frac{7}{3}e^{2} - \frac{8}{3}e - 15$ |
73 | $[73, 73, -2w - 1]$ | $\phantom{-}\frac{4}{9}e^{3} - \frac{5}{3}e^{2} - \frac{17}{3}e + 9$ |
73 | $[73, 73, 2w^{2} + w - 5]$ | $\phantom{-}e^{3} - \frac{14}{3}e^{2} - 4e + 14$ |
83 | $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ | $-\frac{1}{3}e^{2} - 2e + 6$ |
83 | $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e^{2} + 3e + 18$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w^{2}+w+2]$ | $-1$ |
$11$ | $[11,11,-w^{2}-w+1]$ | $1$ |