Base field 4.4.18097.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[12, 6, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w]$ |
Dimension: | $5$ |
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:
\(x^{5} - 5x^{4} - 5x^{3} + 51x^{2} - 54x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 1]$ | $\phantom{-}1$ |
4 | $[4, 2, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ | $\phantom{-}1$ |
7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ | $-e^{4} + 2e^{3} + 10e^{2} - 19e + 4$ |
13 | $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + \frac{11}{2}e + 2$ |
17 | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ | $\phantom{-}e^{4} - e^{3} - 11e^{2} + 9e + 4$ |
27 | $[27, 3, -w^{3} + 7w + 1]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + \frac{7}{2}e^{2} - \frac{29}{2}e + 10$ |
31 | $[31, 31, w + 3]$ | $-\frac{3}{2}e^{4} + \frac{5}{2}e^{3} + \frac{31}{2}e^{2} - \frac{47}{2}e + 3$ |
31 | $[31, 31, -w^{2} + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{11}{2}e^{2} + \frac{31}{2}e - 1$ |
37 | $[37, 37, w^{2} - 3]$ | $\phantom{-}e^{4} - 2e^{3} - 9e^{2} + 18e - 10$ |
41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{9}{2}e^{2} - \frac{7}{2}e + 5$ |
47 | $[47, 47, w^{3} - 5w - 3]$ | $\phantom{-}\frac{5}{2}e^{4} - \frac{9}{2}e^{3} - \frac{53}{2}e^{2} + \frac{91}{2}e - 5$ |
53 | $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ | $-e^{3} + 11e - 4$ |
61 | $[61, 61, w^{3} - w^{2} - 5w + 3]$ | $\phantom{-}\frac{5}{2}e^{4} - \frac{11}{2}e^{3} - \frac{51}{2}e^{2} + \frac{113}{2}e - 10$ |
83 | $[83, 83, w^{3} + w^{2} - 6w - 7]$ | $-\frac{3}{2}e^{4} + \frac{3}{2}e^{3} + \frac{35}{2}e^{2} - \frac{31}{2}e - 6$ |
83 | $[83, 83, -w^{3} + 5w + 1]$ | $-3e^{4} + 6e^{3} + 30e^{2} - 59e + 18$ |
83 | $[83, 83, 2w - 1]$ | $\phantom{-}e^{3} - 9e + 4$ |
83 | $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ | $-\frac{3}{2}e^{4} + \frac{3}{2}e^{3} + \frac{31}{2}e^{2} - \frac{29}{2}e + 7$ |
89 | $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ | $-e^{4} + e^{3} + 12e^{2} - 10e - 12$ |
89 | $[89, 89, w^{3} - 5w + 5]$ | $-\frac{5}{2}e^{4} + \frac{5}{2}e^{3} + \frac{57}{2}e^{2} - \frac{51}{2}e - 13$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w + 1]$ | $-1$ |
$4$ | $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ | $-1$ |