Properties

Label 6.6.592661.1-53.1-e
Base field 6.6.592661.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$
Dimension $4$
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: $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$
Dimension: $4$
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:

\(x^{4} + 2x^{3} - 13x^{2} - 14x + 44\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w^{5} - 5w^{3} + 4w]$ $\phantom{-}e$
13 $[13, 13, -w^{3} + 3w]$ $-e^{2} - 2e + 8$
25 $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 9$
31 $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - \frac{3}{2}e - 8$
31 $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}e^{3} - 9e + 4$
37 $[37, 37, w^{4} - 5w^{2} + w + 3]$ $\phantom{-}3e^{2} + 4e - 20$
43 $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ $-\frac{1}{2}e^{3} + e^{2} + \frac{9}{2}e - 11$
47 $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e + 2$
49 $[49, 7, -w^{4} + 4w^{2} + w - 3]$ $-\frac{3}{2}e^{3} - 2e^{2} + \frac{23}{2}e + 4$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $-1$
59 $[59, 59, w^{4} - 5w^{2} - w + 5]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - \frac{5}{2}e + 1$
61 $[61, 61, w^{3} - w^{2} - 3w]$ $\phantom{-}e^{2} + 2e - 6$
64 $[64, 2, -2]$ $-e^{2} - 3e + 7$
67 $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ $-\frac{1}{2}e^{3} - e^{2} + \frac{9}{2}e + 10$
67 $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ $\phantom{-}e^{3} + 2e^{2} - 8e - 4$
73 $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ $\phantom{-}e^{3} + 2e^{2} - 5e - 8$
73 $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ $\phantom{-}e^{3} - 9e + 2$
83 $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ $\phantom{-}\frac{3}{2}e^{3} + 3e^{2} - \frac{23}{2}e - 11$
97 $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ $-6e^{2} - 6e + 46$
101 $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ $\phantom{-}e^{3} - 7e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $1$