Base field 4.4.2225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[64,8,w^{3} - 2w^{2} - 2w + 5]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w]$ | $\phantom{-}3$ |
4 | $[4, 2, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 1]$ | $\phantom{-}0$ |
19 | $[19, 19, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + 4]$ | $\phantom{-}4$ |
19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - 1]$ | $\phantom{-}4$ |
25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}2$ |
29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{3}{2}w - 1]$ | $-6$ |
29 | $[29, 29, -w^{2} + 5]$ | $\phantom{-}2$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}0$ |
31 | $[31, 31, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $\phantom{-}0$ |
41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w]$ | $-2$ |
41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{1}{2}w - 5]$ | $-10$ |
59 | $[59, 59, w^{3} - w^{2} - 5w + 1]$ | $-4$ |
59 | $[59, 59, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 1]$ | $-12$ |
61 | $[61, 61, \frac{3}{2}w^{3} - \frac{1}{2}w^{2} - \frac{11}{2}w - 2]$ | $\phantom{-}10$ |
61 | $[61, 61, -2w^{2} + w + 7]$ | $\phantom{-}2$ |
71 | $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{5}{2}w + 6]$ | $\phantom{-}16$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} - \frac{1}{2}w - 5]$ | $-16$ |
71 | $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 5]$ | $-8$ |
71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $-8$ |
81 | $[81, 3, -3]$ | $-14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,-\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 1]$ | $1$ |