Base field 4.4.19525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ |
| Dimension: | $19$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{19} - 6x^{18} - 34x^{17} + 264x^{16} + 266x^{15} - 4364x^{14} + 2747x^{13} + 32557x^{12} - 52997x^{11} - 95163x^{10} + 275170x^{9} - 13222x^{8} - 477317x^{7} + 358851x^{6} + 183758x^{5} - 298401x^{4} + 64537x^{3} + 36518x^{2} - 12908x - 200\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $...$ |
| 5 | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w + 3]$ | $...$ |
| 9 | $[9, 3, w + 2]$ | $...$ |
| 11 | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ | $...$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ | $-1$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ | $...$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $...$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ | $...$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ | $...$ |
| 49 | $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ | $...$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ | $...$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ | $...$ |
| 59 | $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ | $...$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ | $...$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ | $...$ |
| 61 | $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ | $...$ |
| 61 | $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 6]$ | $1$ |