Base field 6.6.1868969.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 8x^{2} + x - 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ |
Dimension: | $18$ |
CM: | no |
Base change: | no |
Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{18} - 5x^{17} - 12x^{16} + 90x^{15} + 20x^{14} - 638x^{13} + 311x^{12} + 2263x^{11} - 1906x^{10} - 4189x^{9} + 4545x^{8} + 3747x^{7} - 5119x^{6} - 1116x^{5} + 2550x^{4} - 234x^{3} - 392x^{2} + 72x + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{2} + 3]$ | $...$ |
17 | $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ | $...$ |
23 | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-1$ |
31 | $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ | $...$ |
32 | $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ | $...$ |
43 | $[43, 43, w^{4} - 5w^{2} + 3]$ | $...$ |
47 | $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ | $...$ |
49 | $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ | $...$ |
53 | $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ | $...$ |
59 | $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $...$ |
71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ | $...$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $...$ |
83 | $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ | $...$ |
83 | $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ | $...$ |
89 | $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ | $...$ |
89 | $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ | $...$ |
89 | $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ | $...$ |
89 | $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ | $...$ |
101 | $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $1$ |