Base field 4.4.15317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[4, 2, -w^{2} + w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 7x^{2} + 3x + 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, -w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{7}{3}e + 1$ |
4 | $[4, 2, -w^{2} + w + 1]$ | $-1$ |
19 | $[19, 19, -w^{3} + 5w + 3]$ | $-\frac{2}{3}e^{3} + \frac{8}{3}e^{2} + \frac{2}{3}e - 8$ |
19 | $[19, 19, w^{3} - 3w^{2} - 2w + 7]$ | $-\frac{2}{3}e^{3} - \frac{4}{3}e^{2} + \frac{14}{3}e + 6$ |
43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$ |
43 | $[43, 43, -w^{3} + w^{2} + 2w - 1]$ | $-e^{3} - e^{2} + 8e + 6$ |
43 | $[43, 43, w^{3} - 2w^{2} - w + 1]$ | $-\frac{1}{3}e^{3} + \frac{7}{3}e^{2} - \frac{8}{3}e - 6$ |
43 | $[43, 43, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{4}{3}e^{3} - \frac{4}{3}e^{2} - \frac{10}{3}e + 4$ |
47 | $[47, 47, -w^{3} + w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e^{2} - \frac{10}{3}e + 10$ |
47 | $[47, 47, w^{3} - 5w - 5]$ | $-\frac{1}{3}e^{3} + \frac{13}{3}e^{2} - \frac{2}{3}e - 11$ |
47 | $[47, 47, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{13}{3}e^{2} + \frac{2}{3}e + 19$ |
47 | $[47, 47, w^{3} - 2w^{2} - w + 3]$ | $-e^{3} + 3e^{2} + 6e - 8$ |
49 | $[49, 7, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{2}{3}e - 2$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 7]$ | $-e^{3} + e^{2} + 6e - 4$ |
53 | $[53, 53, 2w - 1]$ | $-2e^{3} + 2e^{2} + 8e + 2$ |
67 | $[67, 67, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{7}{3}e^{3} - \frac{13}{3}e^{2} - \frac{28}{3}e + 7$ |
67 | $[67, 67, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{5}{3}e^{3} + \frac{1}{3}e^{2} - \frac{20}{3}e - 9$ |
81 | $[81, 3, -3]$ | $-\frac{7}{3}e^{3} + \frac{7}{3}e^{2} + \frac{28}{3}e - 1$ |
83 | $[83, 83, 2w^{3} - 4w^{2} - 6w + 9]$ | $-\frac{1}{3}e^{3} + \frac{13}{3}e^{2} - \frac{14}{3}e - 13$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} + w + 1]$ | $1$ |