Properties

Label 6.6.810448.1-64.1-d
Base field 6.6.810448.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $64$
Level $[64, 2, 2]$
Dimension $4$
CM no
Base change yes

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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 $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{7}{8}e^{2} - \frac{31}{8}e + \frac{61}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ $1$