Base field 4.4.5725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 11\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[29,29,-\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 3x - 7\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ | $\phantom{-}e$ |
9 | $[9, 3, -w + 1]$ | $\phantom{-}2$ |
11 | $[11, 11, w]$ | $-e - 1$ |
11 | $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ | $-e - 1$ |
11 | $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ | $\phantom{-}6$ |
11 | $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ | $\phantom{-}e + 4$ |
16 | $[16, 2, 2]$ | $-1$ |
25 | $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ | $\phantom{-}2e + 6$ |
29 | $[29, 29, -w - 3]$ | $-2e - 2$ |
29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $-1$ |
31 | $[31, 31, w^{3} - 6w + 1]$ | $\phantom{-}4$ |
31 | $[31, 31, w^{3} - 6w - 2]$ | $-e - 3$ |
41 | $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ | $\phantom{-}e + 10$ |
41 | $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ | $\phantom{-}e - 5$ |
59 | $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ | $\phantom{-}e - 2$ |
59 | $[59, 59, w^{3} + w^{2} - 6w - 4]$ | $\phantom{-}0$ |
79 | $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ | $\phantom{-}2e + 12$ |
79 | $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ | $-5e - 7$ |
89 | $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ | $-4e - 4$ |
89 | $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ | $\phantom{-}3e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29,29,-\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ | $1$ |