Properties

Label 6.6.1528713.1-53.1-d
Base field 6.6.1528713.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $53$
Level $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$
Dimension $19$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.1528713.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$
Dimension: $19$
CM: no
Base change: no
Newspace dimension: $53$

Hecke eigenvalues ($q$-expansion)

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

\(x^{19} + 8x^{18} - 40x^{17} - 447x^{16} + 306x^{15} + 9513x^{14} + 6101x^{13} - 100431x^{12} - 122404x^{11} + 574563x^{10} + 849961x^{9} - 1846617x^{8} - 2874049x^{7} + 3294888x^{6} + 4877836x^{5} - 3043119x^{4} - 3730437x^{3} + 1267581x^{2} + 906633x - 238383\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, w^{5} - 4w^{4} + 9w^{2} - w - 3]$ $...$
8 $[8, 2, w^{4} - 3w^{3} - 2w^{2} + 5w]$ $\phantom{-}e$
9 $[9, 3, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 1]$ $...$
19 $[19, 19, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 3w + 1]$ $...$
19 $[19, 19, -w + 2]$ $...$
37 $[37, 37, 2w^{5} - 6w^{4} - 5w^{3} + 11w^{2} + 3w - 2]$ $...$
37 $[37, 37, -w^{3} + 3w^{2} + w - 3]$ $...$
53 $[53, 53, -w^{5} + 2w^{4} + 4w^{3} - 2w - 2]$ $-1$
53 $[53, 53, 2w^{5} - 7w^{4} - 2w^{3} + 14w^{2} - 2w - 5]$ $...$
53 $[53, 53, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 3]$ $...$
53 $[53, 53, -4w^{5} + 14w^{4} + 4w^{3} - 27w^{2} + 4w + 6]$ $...$
71 $[71, 71, -w^{5} + 2w^{4} + 5w^{3} - 3w^{2} - 3w - 1]$ $...$
71 $[71, 71, 2w^{5} - 8w^{4} + w^{3} + 16w^{2} - 7w - 6]$ $...$
73 $[73, 73, -3w^{5} + 10w^{4} + 5w^{3} - 20w^{2} - 2w + 6]$ $...$
73 $[73, 73, -w^{5} + 3w^{4} + 2w^{3} - 4w^{2} - 2]$ $...$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 2]$ $...$
73 $[73, 73, w^{4} - 2w^{3} - 5w^{2} + 4w + 4]$ $...$
89 $[89, 89, -w^{5} + 3w^{4} + 2w^{3} - 5w^{2} + 3]$ $...$
89 $[89, 89, 3w^{5} - 10w^{4} - 5w^{3} + 21w^{2} - 5]$ $...$
107 $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-w^{5}+2w^{4}+4w^{3}-2w-2]$ $1$