Base field 4.4.15188.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 4, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
2 | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $\phantom{-}1$ |
11 | $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ | $\phantom{-}3$ |
11 | $[11, 11, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}0$ |
13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}1$ |
19 | $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ | $\phantom{-}7$ |
23 | $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ | $-3$ |
31 | $[31, 31, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}4$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $\phantom{-}4$ |
43 | $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ | $\phantom{-}7$ |
67 | $[67, 67, w^{2} - w - 5]$ | $-13$ |
67 | $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ | $\phantom{-}4$ |
73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}2$ |
79 | $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ | $-4$ |
81 | $[81, 3, -3]$ | $-5$ |
83 | $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ | $\phantom{-}9$ |
83 | $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ | $\phantom{-}15$ |
89 | $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ | $-12$ |
89 | $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ | $\phantom{-}0$ |
97 | $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |
$2$ | $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ | $-1$ |