Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 59x^{4} + 896x^{2} - 768\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w]$ | $-\frac{1}{8}e^{4} + \frac{27}{8}e^{2} + 4$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{3}{64}e^{5} + \frac{97}{64}e^{3} - \frac{17}{4}e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-\frac{3}{64}e^{5} + \frac{97}{64}e^{3} - \frac{17}{4}e$ |
| 27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{89}{8}e^{2} + 8$ |
| 27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}\frac{3}{8}e^{4} - \frac{89}{8}e^{2} + 8$ |
| 29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $-\frac{1}{64}e^{5} + \frac{43}{64}e^{3} - \frac{29}{4}e$ |
| 29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $-\frac{1}{64}e^{5} + \frac{43}{64}e^{3} - \frac{29}{4}e$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{31}{4}e^{2} + 12$ |
| 41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $-\frac{3}{64}e^{5} + \frac{65}{64}e^{3} + \frac{41}{4}e$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $-\frac{3}{64}e^{5} + \frac{65}{64}e^{3} + \frac{41}{4}e$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{31}{4}e^{2} + 12$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $\phantom{-}\frac{1}{32}e^{5} - \frac{43}{32}e^{3} + \frac{23}{2}e$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $\phantom{-}\frac{1}{32}e^{5} - \frac{43}{32}e^{3} + \frac{23}{2}e$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{31}{4}e^{2} + 20$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $\phantom{-}\frac{3}{64}e^{5} - \frac{65}{64}e^{3} - \frac{37}{4}e$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $\phantom{-}\frac{9}{64}e^{5} - \frac{291}{64}e^{3} + \frac{55}{4}e$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{9}{64}e^{5} - \frac{291}{64}e^{3} + \frac{55}{4}e$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}\frac{3}{64}e^{5} - \frac{65}{64}e^{3} - \frac{37}{4}e$ |
| 113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $\phantom{-}\frac{5}{64}e^{5} - \frac{119}{64}e^{3} - \frac{49}{4}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).