Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ |
| Dimension: | $29$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{29} - 2x^{28} - 58x^{27} + 112x^{26} + 1484x^{25} - 2764x^{24} - 22030x^{23} + 39547x^{22} + 209977x^{21} - 363176x^{20} - 1343563x^{19} + 2239363x^{18} + 5867170x^{17} - 9431163x^{16} - 17461334x^{15} + 27109891x^{14} + 34899637x^{13} - 52438525x^{12} - 45677018x^{11} + 66551074x^{10} + 37800842x^{9} - 53464166x^{8} - 18781660x^{7} + 25762645x^{6} + 5122708x^{5} - 6803138x^{4} - 626009x^{3} + 825203x^{2} + 16053x - 30851\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $...$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $...$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, -w + 2]$ | $...$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-1$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $...$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $...$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $...$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $...$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $...$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $...$ |
| 53 | $[53, 53, -w - 3]$ | $...$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $...$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $...$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $...$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $...$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $1$ |