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: | $[23,23,-w^{2} + 2w + 5]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 16x^{4} + 25x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}e$ |
9 | $[9, 3, w^{3} - w^{2} - 5w - 1]$ | $-\frac{1}{10}e^{5} + \frac{6}{5}e^{3} + \frac{23}{10}e$ |
11 | $[11, 11, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{17}{5}e^{2} + \frac{12}{5}$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{29}{5}e^{3} + \frac{9}{5}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{9}{10}e^{5} + \frac{69}{5}e^{3} - \frac{133}{10}e$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{9}{10}e^{5} - \frac{69}{5}e^{3} + \frac{133}{10}e$ |
23 | $[23, 23, w^{2} - 2w - 2]$ | $-\frac{2}{5}e^{5} + \frac{29}{5}e^{3} - \frac{14}{5}e$ |
23 | $[23, 23, w^{3} - w^{2} - 6w - 3]$ | $-\frac{2}{5}e^{4} + \frac{29}{5}e^{2} - \frac{44}{5}$ |
23 | $[23, 23, -w^{2} + 2w + 5]$ | $\phantom{-}1$ |
23 | $[23, 23, -w + 2]$ | $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} - \frac{47}{5}e$ |
37 | $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ | $\phantom{-}\frac{4}{5}e^{4} - \frac{63}{5}e^{2} + \frac{28}{5}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ | $-\frac{7}{10}e^{5} + \frac{52}{5}e^{3} - \frac{49}{10}e$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ | $-\frac{3}{10}e^{5} + \frac{23}{5}e^{3} - \frac{61}{10}e$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{12}{5}e^{2} - \frac{8}{5}$ |
47 | $[47, 47, w^{2} - 2w - 1]$ | $\phantom{-}e^{5} - 15e^{3} + 10e$ |
47 | $[47, 47, w^{2} - 2w - 6]$ | $-e^{4} + 15e^{2} - 16$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}\frac{2}{5}e^{5} - \frac{29}{5}e^{3} + \frac{9}{5}e$ |
59 | $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ | $\phantom{-}\frac{4}{5}e^{4} - \frac{58}{5}e^{2} + \frac{8}{5}$ |
73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-\frac{1}{5}e^{4} + \frac{17}{5}e^{2} - \frac{2}{5}$ |
83 | $[83, 83, -w^{3} + w^{2} + 4w + 3]$ | $-\frac{4}{5}e^{5} + \frac{63}{5}e^{3} - \frac{68}{5}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23,23,-w^{2} + 2w + 5]$ | $-1$ |