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: | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 55x^{4} + 718x^{2} - 999\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $-\frac{1}{615}e^{4} - \frac{37}{615}e^{2} + \frac{676}{205}$ |
9 | $[9, 3, w^{3} - w^{2} - 5w - 1]$ | $-\frac{8}{615}e^{4} + \frac{319}{615}e^{2} - \frac{127}{205}$ |
11 | $[11, 11, -w^{3} + w^{2} + 6w + 2]$ | $\phantom{-}\frac{1}{123}e^{5} - \frac{15}{41}e^{3} + \frac{350}{123}e$ |
11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $-1$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{615}e^{4} + \frac{37}{615}e^{2} + \frac{349}{205}$ |
23 | $[23, 23, w^{2} - 2w - 2]$ | $\phantom{-}\frac{2}{615}e^{5} - \frac{131}{615}e^{3} + \frac{1274}{615}e$ |
23 | $[23, 23, w^{3} - w^{2} - 6w - 3]$ | $-\frac{1}{205}e^{5} + \frac{94}{615}e^{3} + \frac{139}{615}e$ |
23 | $[23, 23, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{123}e^{5} - \frac{15}{41}e^{3} + \frac{473}{123}e$ |
23 | $[23, 23, -w + 2]$ | $\phantom{-}\frac{1}{615}e^{5} + \frac{37}{615}e^{3} - \frac{676}{205}e$ |
37 | $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ | $\phantom{-}\frac{17}{615}e^{4} - \frac{601}{615}e^{2} + \frac{1013}{205}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ | $-\frac{2}{123}e^{4} + \frac{49}{123}e^{2} + \frac{122}{41}$ |
37 | $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ | $\phantom{-}\frac{11}{205}e^{4} - \frac{413}{205}e^{2} + \frac{2497}{205}$ |
37 | $[37, 37, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{26}{615}e^{4} + \frac{883}{615}e^{2} - \frac{874}{205}$ |
47 | $[47, 47, w^{2} - 2w - 1]$ | $-\frac{1}{615}e^{5} - \frac{37}{615}e^{3} + \frac{471}{205}e$ |
47 | $[47, 47, w^{2} - 2w - 6]$ | $-\frac{11}{615}e^{5} + \frac{206}{205}e^{3} - \frac{7417}{615}e$ |
59 | $[59, 59, 2w - 1]$ | $-\frac{1}{615}e^{5} - \frac{37}{615}e^{3} + \frac{676}{205}e$ |
59 | $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ | $-\frac{11}{615}e^{5} + \frac{206}{205}e^{3} - \frac{6802}{615}e$ |
73 | $[73, 73, -w^{3} + w^{2} + 7w + 1]$ | $-\frac{9}{205}e^{4} + \frac{282}{205}e^{2} - \frac{1018}{205}$ |
83 | $[83, 83, -w^{3} + w^{2} + 4w + 3]$ | $-\frac{8}{615}e^{5} + \frac{524}{615}e^{3} - \frac{8786}{615}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $1$ |