Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} - w + 4]$ |
| Dimension: | $35$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{35} + 5x^{34} - 60x^{33} - 324x^{32} + 1576x^{31} + 9388x^{30} - 23764x^{29} - 160864x^{28} + 226129x^{27} + 1816859x^{26} - 1398492x^{25} - 14275384x^{24} + 5500529x^{23} + 80298929x^{22} - 12132850x^{21} - 327915044x^{20} + 5288892x^{19} + 975536814x^{18} + 48241475x^{17} - 2101203841x^{16} - 140014166x^{15} + 3220298888x^{14} + 171099190x^{13} - 3400184170x^{12} - 87998330x^{11} + 2343221628x^{10} + 4037987x^{9} - 964625761x^{8} + 4318180x^{7} + 203728052x^{6} + 1644927x^{5} - 15779489x^{4} + 93648x^{3} + 358984x^{2} - 22640x + 112\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $...$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $...$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $...$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, -w]$ | $...$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $...$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $...$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $...$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $...$ |
| 47 | $[47, 47, w^{2} - 6]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $...$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $...$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $...$ |
| 61 | $[61, 61, w^{2} - 5]$ | $...$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $...$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $...$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} - w + 4]$ | $-1$ |