Base field 4.4.13025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 3x + 29\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{11}{2}]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 8x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} + w + 8]$ | $-1$ |
5 | $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ | $\phantom{-}1$ |
5 | $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ | $-e^{2} - 2e + 1$ |
19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ | $-e^{2} - 4e - 1$ |
19 | $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ | $\phantom{-}e^{3} + 3e^{2} - e - 5$ |
29 | $[29, 29, w]$ | $-2e^{3} - 6e^{2} + 4e + 10$ |
29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ | $\phantom{-}2e^{2} + 4e - 4$ |
29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ | $\phantom{-}2e^{3} + 5e^{2} - 8e - 11$ |
29 | $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ | $-2e^{3} - 6e^{2} + 6e + 12$ |
41 | $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ | $-e^{3} - 2e^{2} + 5e - 2$ |
41 | $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ | $\phantom{-}e^{3} + 3e^{2} + e - 3$ |
61 | $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ | $\phantom{-}3e^{3} + 9e^{2} - 11e - 17$ |
61 | $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ | $-3e^{3} - 8e^{2} + 11e + 12$ |
79 | $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ | $-2e^{3} - 7e^{2} + 2e + 3$ |
79 | $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ | $\phantom{-}2e^{3} + 8e^{2} - 4e - 14$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e^{3} + 7e^{2} - 4e - 13$ |
89 | $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ | $-e^{3} + 9e - 8$ |
89 | $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ | $-e^{3} - 3e^{2} + 3e + 3$ |
109 | $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ | $\phantom{-}2e^{3} + 6e^{2} - 8e - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} + w + 8]$ | $1$ |
$5$ | $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ | $-1$ |