Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ |
Dimension: | $18$ |
CM: | no |
Base change: | no |
Newspace dimension: | $45$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{18} - 11x^{17} - 70x^{16} + 1131x^{15} + 659x^{14} - 44766x^{13} + 55708x^{12} + 899574x^{11} - 1935797x^{10} - 9956434x^{9} + 27400699x^{8} + 60057286x^{7} - 199119181x^{6} - 170723409x^{5} + 730945516x^{4} + 78612582x^{3} - 1070512488x^{2} + 400456088x - 13089752\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $...$ |
11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
11 | $[11, 11, w - 1]$ | $...$ |
19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $...$ |
19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $...$ |
29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $...$ |
29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $...$ |
29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $...$ |
29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $...$ |
31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $-1$ |
41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $...$ |
59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $...$ |
61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $...$ |
61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $...$ |
61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $...$ |
61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $...$ |
64 | $[64, 2, -2]$ | $...$ |
79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $...$ |
89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $...$ |
101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $1$ |