Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[19, 19, -w^{2} + 6]$ |
Dimension: | $19$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{19} - 10x^{18} - 31x^{17} + 557x^{16} - 299x^{15} - 10638x^{14} + 15837x^{13} + 92616x^{12} - 145469x^{11} - 470115x^{10} + 540469x^{9} + 1470025x^{8} - 760970x^{7} - 2531686x^{6} + 21836x^{5} + 1999540x^{4} + 624949x^{3} - 462855x^{2} - 207947x + 886\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $...$ |
9 | $[9, 3, -w^{3} + 8w + 8]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $...$ |
19 | $[19, 19, w + 1]$ | $...$ |
19 | $[19, 19, -w^{2} + 6]$ | $-1$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $...$ |
19 | $[19, 19, -w + 2]$ | $...$ |
25 | $[25, 5, 2w^{2} - 2w - 13]$ | $...$ |
29 | $[29, 29, -w^{2} + 9]$ | $...$ |
29 | $[29, 29, -w^{2} + 2w + 6]$ | $...$ |
29 | $[29, 29, w^{2} - 7]$ | $...$ |
29 | $[29, 29, -w^{2} + 2w + 8]$ | $...$ |
31 | $[31, 31, -2w^{2} + w + 12]$ | $...$ |
31 | $[31, 31, 2w^{2} - 3w - 11]$ | $...$ |
41 | $[41, 41, -w]$ | $...$ |
41 | $[41, 41, -w + 1]$ | $...$ |
49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $...$ |
49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $...$ |
61 | $[61, 61, 2w^{2} - 3w - 14]$ | $...$ |
61 | $[61, 61, 2w^{2} - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{2} + 6]$ | $1$ |