Properties

Label 6.6.1767625.1-44.1-f
Base field 6.6.1767625.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, w^{2} - w - 2]$
Dimension $4$
CM no
Base change no

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Base field 6.6.1767625.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[44, 22, w^{2} - w - 2]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $44$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{4} - 4x^{3} - 10x^{2} + 28x + 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w + 1]$ $-1$
9 $[9, 3, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{3}{2}w^{2} - 5w + \frac{1}{2}]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ $\phantom{-}1$
16 $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ $\phantom{-}e$
29 $[29, 29, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 4w^{3} + \frac{5}{2}w^{2} - 6w + \frac{1}{2}]$ $-\frac{1}{4}e^{3} + \frac{5}{4}e^{2} + \frac{3}{4}e - \frac{23}{4}$
41 $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{3}{2}w^{2} + 3w + \frac{3}{2}]$ $\phantom{-}\frac{1}{2}e^{2} - 2e - \frac{7}{2}$
41 $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 2w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}]$ $-e^{2} + 2e + 7$
59 $[59, 59, -\frac{3}{2}w^{5} + \frac{1}{2}w^{4} + 9w^{3} + \frac{1}{2}w^{2} - 11w - \frac{5}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{11}{2}e + 10$
59 $[59, 59, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 3w^{3} + \frac{5}{2}w^{2} - 4w - \frac{1}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{7}{2}e + 6$
59 $[59, 59, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 2w^{3} - \frac{1}{2}w^{2} - \frac{3}{2}]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 1$
59 $[59, 59, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 11w - \frac{1}{2}]$ $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - \frac{7}{2}e + 6$
61 $[61, 61, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{1}{2}w^{2} + 4w + \frac{5}{2}]$ $-\frac{1}{2}e^{2} + 2e - \frac{5}{2}$
71 $[71, 71, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 5w^{3} + \frac{5}{2}w^{2} - 11w - \frac{3}{2}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{4}e^{2} - \frac{11}{4}e + \frac{45}{4}$
71 $[71, 71, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 4w^{3} - \frac{5}{2}w^{2} - 7w + \frac{3}{2}]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{15}{2}e - \frac{25}{2}$
79 $[79, 79, -w^{5} + 6w^{3} + 2w^{2} - 8w - 2]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{15}{2}e - \frac{29}{2}$
79 $[79, 79, -\frac{3}{2}w^{5} + \frac{3}{2}w^{4} + 9w^{3} - \frac{11}{2}w^{2} - 12w + \frac{3}{2}]$ $\phantom{-}e^{3} - 3e^{2} - 11e + 11$
81 $[81, 3, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 8w + \frac{3}{2}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{19}{4}e + \frac{25}{4}$
89 $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 14w + \frac{7}{2}]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{3}{4}e - \frac{25}{4}$
89 $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 10w - \frac{1}{2}]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{19}{4}e - \frac{19}{4}$
89 $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 15w + \frac{9}{2}]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 11$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, w + 1]$ $1$
$11$ $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ $-1$