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 | $[107, 107, 2w^{5} - 6w^{4} - 5w^{3} + 12w^{2} + 2w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$53$ | $[53,53,-w^{5}+2w^{4}+4w^{3}-2w-2]$ | $1$ |