Base field 6.6.1134389.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 6x^{3} + 4x^{2} - 3x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 28x^{4} + 217x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{3}{4}e^{5} - 17e^{3} + \frac{283}{4}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - \frac{65}{8}e$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-1$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ | $\phantom{-}\frac{7}{8}e^{5} - \frac{39}{2}e^{3} + \frac{639}{8}e$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{4}e^{5} - 6e^{3} + \frac{113}{4}e$ |
| 37 | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}2e^{4} - 45e^{2} + 186$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ | $-\frac{3}{8}e^{5} + \frac{17}{2}e^{3} - \frac{299}{8}e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}e^{4} - 22e^{2} + 96$ |
| 64 | $[64, 2, -2]$ | $-3e^{4} + 67e^{2} - 275$ |
| 67 | $[67, 67, 2w - 1]$ | $-2e^{2} + 20$ |
| 79 | $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ | $-\frac{11}{8}e^{5} + \frac{61}{2}e^{3} - \frac{995}{8}e$ |
| 79 | $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ | $\phantom{-}\frac{7}{8}e^{5} - \frac{39}{2}e^{3} + \frac{615}{8}e$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ | $\phantom{-}3e^{4} - 66e^{2} + 270$ |
| 97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ | $-\frac{1}{8}e^{5} + \frac{5}{2}e^{3} - \frac{65}{8}e$ |
| 101 | $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ | $-\frac{3}{8}e^{5} + \frac{17}{2}e^{3} - \frac{315}{8}e$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ | $-\frac{3}{4}e^{5} + 17e^{3} - \frac{275}{4}e$ |
| 103 | $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ | $-\frac{9}{8}e^{5} + \frac{51}{2}e^{3} - \frac{865}{8}e$ |
| 107 | $[107, 107, w^{2} - 2w - 3]$ | $-2e^{4} + 45e^{2} - 196$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w^{4}+w^{3}+4w^{2}-2w-2]$ | $1$ |