Base field 6.6.1416125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 5x^{4} + 9x^{3} + 6x^{2} - 9x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ |
Dimension: | $16$ |
CM: | no |
Base change: | no |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} + 5x^{15} - 34x^{14} - 194x^{13} + 346x^{12} + 2633x^{11} - 1004x^{10} - 16838x^{9} - 3708x^{8} + 54656x^{7} + 29001x^{6} - 87412x^{5} - 61533x^{4} + 60755x^{3} + 48257x^{2} - 14845x - 12565\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w^{4} + 2w^{3} + 3w^{2} - 5w]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{3} - w^{2} - 4w + 2]$ | $...$ |
19 | $[19, 19, -w^{3} + 4w]$ | $...$ |
19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 6w + 3]$ | $...$ |
19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 3]$ | $...$ |
25 | $[25, 5, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 5]$ | $...$ |
29 | $[29, 29, -w^{3} + 4w + 1]$ | $...$ |
41 | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $\phantom{-}1$ |
49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 8w - 4]$ | $...$ |
59 | $[59, 59, -w^{4} + 3w^{3} + 2w^{2} - 8w + 2]$ | $...$ |
59 | $[59, 59, -w^{3} + w^{2} + 2w - 3]$ | $...$ |
61 | $[61, 61, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 4w - 2]$ | $...$ |
64 | $[64, 2, -2]$ | $...$ |
71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 4w + 1]$ | $...$ |
71 | $[71, 71, 2w^{4} - 3w^{3} - 5w^{2} + 6w]$ | $...$ |
79 | $[79, 79, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} + w - 4]$ | $...$ |
79 | $[79, 79, w^{4} - 3w^{3} - w^{2} + 8w - 3]$ | $...$ |
89 | $[89, 89, w^{5} - 6w^{3} - w^{2} + 8w]$ | $...$ |
109 | $[109, 109, -w^{5} + 2w^{4} + 3w^{3} - 6w^{2} - 2w + 5]$ | $...$ |
109 | $[109, 109, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 13w + 11]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$41$ | $[41, 41, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ | $-1$ |