Base field 3.3.1937.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[19, 19, -w^{2} + 2w + 4]$ |
Dimension: | $31$ |
CM: | no |
Base change: | no |
Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{31} - 6x^{30} - 41x^{29} + 293x^{28} + 687x^{27} - 6321x^{26} - 5835x^{25} + 79726x^{24} + 22615x^{23} - 655236x^{22} + 18208x^{21} + 3698066x^{20} - 598155x^{19} - 14692150x^{18} + 2714593x^{17} + 41337624x^{16} - 5606986x^{15} - 81497072x^{14} + 3628191x^{13} + 109443769x^{12} + 6656685x^{11} - 95471494x^{10} - 14850682x^{9} + 50665818x^{8} + 11319528x^{7} - 14970223x^{6} - 3829211x^{5} + 2165635x^{4} + 526733x^{3} - 121378x^{2} - 16677x + 2714\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $...$ |
7 | $[7, 7, w - 3]$ | $...$ |
8 | $[8, 2, 2]$ | $...$ |
9 | $[9, 3, w^{2} - 3w - 2]$ | $...$ |
13 | $[13, 13, w + 3]$ | $...$ |
13 | $[13, 13, -w + 2]$ | $...$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}1$ |
23 | $[23, 23, w^{2} - 4w + 1]$ | $...$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $...$ |
31 | $[31, 31, w^{2} - 2w - 9]$ | $...$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $...$ |
41 | $[41, 41, w^{2} - w - 1]$ | $...$ |
41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
41 | $[41, 41, w^{2} - w - 10]$ | $...$ |
43 | $[43, 43, -2w - 3]$ | $...$ |
47 | $[47, 47, -w^{2} - w + 4]$ | $...$ |
49 | $[49, 7, -w^{2} + 5w - 5]$ | $...$ |
59 | $[59, 59, w^{2} - w - 4]$ | $...$ |
59 | $[59, 59, w^{2} - 3]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{2} + 2w + 4]$ | $-1$ |