Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[1, 1, 1]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 16x^{4} + 76x^{2} - 92\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + 10e$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{5} + 4e^{3} - 4e$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{1}{2}e^{5} + 4e^{3} - 4e$ |
13 | $[13, 13, w^{3} - 4w + 1]$ | $-e^{4} + 10e^{2} - 20$ |
13 | $[13, 13, -w^{3} + 4w + 1]$ | $-e^{4} + 10e^{2} - 20$ |
25 | $[25, 5, -w^{2} - 2w + 1]$ | $\phantom{-}2e^{4} - 18e^{2} + 26$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}2e^{4} - 18e^{2} + 26$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $-3e^{4} + 28e^{2} - 46$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $-3e^{4} + 28e^{2} - 46$ |
59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} - 6e$ |
59 | $[59, 59, -w^{2} - w + 5]$ | $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} - 6e$ |
61 | $[61, 61, -w^{3} + w^{2} + 4w - 7]$ | $\phantom{-}3e^{4} - 28e^{2} + 46$ |
61 | $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ | $\phantom{-}3e^{4} - 28e^{2} + 46$ |
73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}3e^{4} - 24e^{2} + 22$ |
73 | $[73, 73, 2w - 1]$ | $\phantom{-}e^{4} - 12e^{2} + 26$ |
73 | $[73, 73, -2w - 1]$ | $\phantom{-}e^{4} - 12e^{2} + 26$ |
73 | $[73, 73, 2w^{2} + w - 5]$ | $\phantom{-}3e^{4} - 24e^{2} + 22$ |
83 | $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ | $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + 20e$ |
83 | $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ | $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + 20e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).