Base field 4.4.13968.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8,2,\frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ | $-1$ |
2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $\phantom{-}0$ |
9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}0$ |
13 | $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ | $-2$ |
13 | $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}4$ |
23 | $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ | $-6$ |
23 | $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ | $-6$ |
37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ | $-2$ |
37 | $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ | $-8$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ | $-12$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ | $-6$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ | $\phantom{-}8$ |
61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}10$ |
61 | $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ | $-8$ |
61 | $[61, 61, w^{3} - w^{2} - 8w + 1]$ | $\phantom{-}2$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ | $-6$ |
71 | $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ | $\phantom{-}12$ |
83 | $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ | $\phantom{-}0$ |
83 | $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ | $\phantom{-}6$ |
97 | $[97, 97, 2w - 1]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,\frac{1}{2}w^{2} - \frac{3}{2}w]$ | $-1$ |
$2$ | $[2,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + 1]$ | $1$ |