Base field 4.4.14725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 11x + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{11}{3}]$ | $\phantom{-}2e + 2$ |
9 | $[9, 3, w - 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{8}{3}]$ | $-3e$ |
11 | $[11, 11, \frac{2}{3}w^{3} + \frac{2}{3}w^{2} - \frac{19}{3}w - \frac{13}{3}]$ | $-2$ |
16 | $[16, 2, 2]$ | $-3e - 1$ |
19 | $[19, 19, w + 2]$ | $-3e + 2$ |
25 | $[25, 5, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{16}{3}w + \frac{13}{3}]$ | $\phantom{-}0$ |
29 | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ | $\phantom{-}1$ |
29 | $[29, 29, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{5}{3}w + \frac{14}{3}]$ | $-2e$ |
29 | $[29, 29, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - \frac{8}{3}]$ | $\phantom{-}3e + 4$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}e - 6$ |
31 | $[31, 31, w]$ | $-3e + 6$ |
31 | $[31, 31, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{8}{3}w + \frac{13}{3}]$ | $-6$ |
31 | $[31, 31, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + \frac{11}{3}w + \frac{5}{3}]$ | $\phantom{-}6e - 2$ |
41 | $[41, 41, \frac{1}{3}w^{3} + \frac{4}{3}w^{2} - \frac{8}{3}w - \frac{20}{3}]$ | $\phantom{-}6e - 2$ |
41 | $[41, 41, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{40}{3}]$ | $\phantom{-}4e - 6$ |
49 | $[49, 7, -\frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{8}{3}w + \frac{38}{3}]$ | $-2e$ |
49 | $[49, 7, \frac{2}{3}w^{3} + \frac{5}{3}w^{2} - \frac{16}{3}w - \frac{43}{3}]$ | $\phantom{-}6e$ |
59 | $[59, 59, \frac{5}{3}w^{3} + \frac{8}{3}w^{2} - \frac{40}{3}w - \frac{49}{3}]$ | $-10$ |
59 | $[59, 59, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - \frac{16}{3}w + \frac{11}{3}]$ | $-4e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, -\frac{2}{3}w^{3} - \frac{2}{3}w^{2} + \frac{19}{3}w + \frac{19}{3}]$ | $-1$ |