Base field 4.4.10512.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - 6x + 1\); narrow class number \(4\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - w^{2} - 5w - 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 28x^{2} + 71\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}\frac{1}{10}e^{2} + \frac{11}{10}$ |
9 | $[9, 3, w^{3} - w^{2} - 5w - 1]$ | $-1$ |
11 | $[11, 11, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{1}{10}e^{2} + \frac{29}{10}$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{10}e^{2} + \frac{29}{10}$ |
23 | $[23, 23, w^{2} - 2w - 2]$ | $-\frac{1}{10}e^{3} + \frac{9}{10}e$ |
23 | $[23, 23, w^{3} - w^{2} - 6w - 3]$ | $-\frac{1}{5}e^{3} + \frac{24}{5}e$ |
23 | $[23, 23, -w^{2} + 2w + 5]$ | $-\frac{1}{10}e^{3} + \frac{9}{10}e$ |
23 | $[23, 23, -w + 2]$ | $-\frac{1}{5}e^{3} + \frac{24}{5}e$ |
37 | $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ | $-\frac{1}{5}e^{2} + \frac{4}{5}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ | $-\frac{1}{10}e^{2} + \frac{69}{10}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ | $-\frac{1}{10}e^{2} + \frac{69}{10}$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{1}{5}e^{2} + \frac{4}{5}$ |
47 | $[47, 47, w^{2} - 2w - 1]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{77}{10}e$ |
47 | $[47, 47, w^{2} - 2w - 6]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{77}{10}e$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{67}{10}e$ |
59 | $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{67}{10}e$ |
73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-\frac{7}{5}e^{2} + \frac{93}{5}$ |
83 | $[83, 83, -w^{3} + w^{2} + 4w + 3]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{29}{5}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, w^{3} - w^{2} - 5w - 1]$ | $1$ |