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 | $[19, 19, -w^{2} + 2w + 4]$ | $-1$ |
| 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 |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + 2w + 4]$ | $1$ |