Base field 6.6.810448.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[64, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 17x^{3} + 79x^{2} - 64x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}0$ |
25 | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ | $-\frac{1}{16}e^{3} + \frac{23}{16}e^{2} - \frac{137}{16}e + \frac{43}{8}$ |
25 | $[25, 5, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - 2w + 2]$ | $-\frac{1}{16}e^{3} + \frac{23}{16}e^{2} - \frac{137}{16}e + \frac{43}{8}$ |
25 | $[25, 5, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}e$ |
27 | $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{8}e^{3} + \frac{15}{8}e^{2} - \frac{57}{8}e + \frac{11}{4}$ |
27 | $[27, 3, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 6w - 4]$ | $-\frac{1}{8}e^{3} + \frac{15}{8}e^{2} - \frac{57}{8}e + \frac{11}{4}$ |
37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 3w + 2]$ | $-\frac{1}{4}e^{3} + \frac{15}{4}e^{2} - \frac{49}{4}e - \frac{1}{2}$ |
37 | $[37, 37, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 5w + 5]$ | $-\frac{3}{16}e^{3} + \frac{37}{16}e^{2} - \frac{107}{16}e + \frac{17}{8}$ |
37 | $[37, 37, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} - 2]$ | $-\frac{3}{16}e^{3} + \frac{37}{16}e^{2} - \frac{107}{16}e + \frac{17}{8}$ |
67 | $[67, 67, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 2]$ | $-\frac{1}{4}e^{3} + \frac{11}{4}e^{2} - \frac{25}{4}e + \frac{11}{2}$ |
67 | $[67, 67, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 7w - 5]$ | $-\frac{1}{4}e^{3} + \frac{11}{4}e^{2} - \frac{25}{4}e + \frac{11}{2}$ |
67 | $[67, 67, -2w^{5} + 6w^{4} + 4w^{3} - 16w^{2} - 3w + 5]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{19}{4}e^{2} + \frac{89}{4}e - \frac{11}{2}$ |
67 | $[67, 67, -2w^{5} + 4w^{4} + 8w^{3} - 12w^{2} - 9w + 6]$ | $\phantom{-}e^{2} - 8e$ |
67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 6w + 4]$ | $\phantom{-}e^{2} - 8e$ |
67 | $[67, 67, w^{5} - 4w^{4} + 10w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{19}{4}e^{2} + \frac{89}{4}e - \frac{11}{2}$ |
107 | $[107, 107, w^{5} - 3w^{4} - w^{3} + 7w^{2} - 3w - 2]$ | $\phantom{-}2e^{2} - 19e + 18$ |
107 | $[107, 107, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 5]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{15}{4}e^{2} + \frac{61}{4}e - \frac{23}{2}$ |
107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 13w^{2} + 6w - 4]$ | $\phantom{-}\frac{1}{8}e^{3} - \frac{7}{8}e^{2} - \frac{31}{8}e + \frac{61}{4}$ |
107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 15w^{2} + 4w - 6]$ | $\phantom{-}2e^{2} - 19e + 18$ |
107 | $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{8}e^{3} - \frac{7}{8}e^{2} - \frac{31}{8}e + \frac{61}{4}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $1$ |