Base field 3.3.316.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, w^{2} - w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 12x^{4} + 12x^{3} + 35x^{2} - 31x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 1]$ | $-\frac{1}{4}e^{5} + \frac{5}{2}e^{3} - \frac{21}{4}e$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $-\frac{1}{4}e^{5} - \frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{7}{2}e^{2} - \frac{25}{4}e - 3$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{5}{2}e^{3} - \frac{9}{2}e^{2} + \frac{21}{4}e + 9$ |
| 19 | $[19, 19, w^{2} - w + 1]$ | $\phantom{-}1$ |
| 23 | $[23, 23, 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{9}{2}e^{2} - \frac{7}{4}e + 9$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}2e - 2$ |
| 29 | $[29, 29, 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{5}{2}e^{3} + \frac{9}{2}e^{2} + \frac{21}{4}e - 3$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{3}{4}e^{5} + \frac{1}{2}e^{4} - \frac{17}{2}e^{3} - \frac{5}{2}e^{2} + \frac{83}{4}e - 1$ |
| 37 | $[37, 37, 2w^{2} - 2w - 5]$ | $-2e^{2} + 8$ |
| 41 | $[41, 41, 2w^{2} - 9]$ | $-\frac{1}{4}e^{5} + \frac{1}{2}e^{4} + \frac{3}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{4}e + 9$ |
| 43 | $[43, 43, w^{2} + w - 5]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{21}{2}e + 2$ |
| 43 | $[43, 43, -3w^{2} + w + 15]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 8$ |
| 43 | $[43, 43, -2w^{2} + 2w + 11]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 10$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $-e^{5} + 11e^{3} - 26e + 6$ |
| 61 | $[61, 61, 4w^{2} - 2w - 15]$ | $-\frac{3}{4}e^{5} - \frac{1}{2}e^{4} + \frac{13}{2}e^{3} + \frac{7}{2}e^{2} - \frac{39}{4}e - 1$ |
| 67 | $[67, 67, -5w^{2} + 3w + 23]$ | $-\frac{3}{4}e^{5} - \frac{3}{2}e^{4} + \frac{15}{2}e^{3} + \frac{21}{2}e^{2} - \frac{67}{4}e - 7$ |
| 73 | $[73, 73, 2w^{2} - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 6e^{3} + 7e^{2} + \frac{27}{2}e - 4$ |
| 73 | $[73, 73, -3w^{2} - w + 7]$ | $-\frac{1}{2}e^{5} + 5e^{3} - 2e^{2} - \frac{17}{2}e + 8$ |
| 73 | $[73, 73, -6w^{2} + 4w + 25]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{1}{2}e^{4} - \frac{5}{2}e^{3} + \frac{7}{2}e^{2} + \frac{9}{4}e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{2} - w + 1]$ | $-1$ |