Properties

Label 6.6.592661.1-59.1-b
Base field 6.6.592661.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $59$
Level $[59, 59, w^{4} - 5w^{2} - w + 5]$
Dimension $3$
CM no
Base change no

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Base field 6.6.592661.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[59, 59, w^{4} - 5w^{2} - w + 5]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 26x - 33\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{5} - 5w^{3} + 4w]$ $-1$
13 $[13, 13, -w^{3} + 3w]$ $\phantom{-}e$
25 $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-\frac{5}{9}e^{2} + \frac{13}{9}e + \frac{19}{3}$
31 $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ $\phantom{-}\frac{1}{9}e^{2} + \frac{1}{9}e - \frac{17}{3}$
31 $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $-\frac{2}{9}e^{2} + \frac{7}{9}e - \frac{8}{3}$
37 $[37, 37, w^{4} - 5w^{2} + w + 3]$ $-\frac{1}{3}e^{2} + \frac{2}{3}e + 2$
43 $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ $-\frac{4}{9}e^{2} - \frac{4}{9}e + \frac{26}{3}$
47 $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ $\phantom{-}\frac{5}{9}e^{2} - \frac{31}{9}e - \frac{28}{3}$
49 $[49, 7, -w^{4} + 4w^{2} + w - 3]$ $\phantom{-}\frac{4}{9}e^{2} - \frac{5}{9}e - \frac{8}{3}$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $\phantom{-}\frac{5}{9}e^{2} - \frac{31}{9}e - \frac{28}{3}$
59 $[59, 59, w^{4} - 5w^{2} - w + 5]$ $\phantom{-}1$
61 $[61, 61, w^{3} - w^{2} - 3w]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 13$
64 $[64, 2, -2]$ $-\frac{2}{9}e^{2} - \frac{11}{9}e + \frac{4}{3}$
67 $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ $\phantom{-}\frac{5}{9}e^{2} + \frac{5}{9}e - \frac{37}{3}$
67 $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ $\phantom{-}e^{2} - 4e - 21$
73 $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ $-e^{2} + 3e + 15$
73 $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - 5$
83 $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ $\phantom{-}\frac{7}{9}e^{2} - \frac{11}{9}e - \frac{23}{3}$
97 $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ $\phantom{-}\frac{10}{9}e^{2} - \frac{53}{9}e - \frac{74}{3}$
101 $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ $-\frac{8}{9}e^{2} + \frac{37}{9}e + \frac{55}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$59$ $[59, 59, w^{4} - 5w^{2} - w + 5]$ $-1$