Properties

Label 6.6.1767625.1-11.1-c
Base field 6.6.1767625.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$
Dimension $2$
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: $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

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

Atkin-Lehner eigenvalues

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