Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 13x^{4} + 46x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 2$ |
4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}0$ |
17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{4}e^{5} + \frac{5}{4}e^{3} + \frac{5}{2}e$ |
17 | $[17, 17, -w + 2]$ | $-\frac{1}{4}e^{5} + \frac{5}{4}e^{3} + \frac{5}{2}e$ |
29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{3}{4}e^{5} + \frac{31}{4}e^{3} - \frac{33}{2}e$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $-\frac{3}{4}e^{5} + \frac{31}{4}e^{3} - \frac{33}{2}e$ |
31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 12$ |
31 | $[31, 31, -w^{3} + 7w + 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 12$ |
41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{13}{4}e^{3} + \frac{15}{2}e$ |
41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{13}{4}e^{3} + \frac{15}{2}e$ |
67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 6$ |
67 | $[67, 67, -w^{2} + 4w + 2]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 6$ |
83 | $[83, 83, 2w^{2} - 5w - 2]$ | $-e^{5} + 7e^{3} - 4e$ |
83 | $[83, 83, -w^{3} + 8w + 6]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 9e$ |
83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $-e^{5} + 7e^{3} - 4e$ |
83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 9e$ |
97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $\phantom{-}\frac{5}{2}e^{4} - \frac{43}{2}e^{2} + 28$ |
97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{5}{2}e^{4} - \frac{43}{2}e^{2} + 28$ |
97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{2} - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $1$ |