Base field 4.4.13625.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 11x^{2} + 12x + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, \frac{1}{2}w^{2} - \frac{3}{2}w - \frac{5}{2}]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{2} - \frac{1}{2}w + \frac{3}{2}]$ | $\phantom{-}1$ |
4 | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $-1$ |
5 | $[5, 5, w - 3]$ | $\phantom{-}1$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 4w - \frac{7}{2}]$ | $\phantom{-}0$ |
11 | $[11, 11, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 7]$ | $\phantom{-}0$ |
19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}4$ |
19 | $[19, 19, -w^{2} + 5]$ | $-2$ |
31 | $[31, 31, w]$ | $-4$ |
31 | $[31, 31, w + 3]$ | $\phantom{-}2$ |
31 | $[31, 31, -w + 4]$ | $-4$ |
31 | $[31, 31, w - 1]$ | $-10$ |
41 | $[41, 41, -w^{2} + 2]$ | $\phantom{-}6$ |
41 | $[41, 41, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{3}{2}w + 12]$ | $-6$ |
59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 5]$ | $\phantom{-}0$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + 2w^{2} + 2w - \frac{17}{2}]$ | $-12$ |
79 | $[79, 79, -w^{2} + 8]$ | $-8$ |
79 | $[79, 79, w^{2} - 2w - 7]$ | $\phantom{-}4$ |
81 | $[81, 3, -3]$ | $\phantom{-}10$ |
101 | $[101, 101, -w^{3} + \frac{1}{2}w^{2} + \frac{15}{2}w + \frac{3}{2}]$ | $\phantom{-}0$ |
101 | $[101, 101, w^{3} - \frac{5}{2}w^{2} - \frac{11}{2}w + \frac{17}{2}]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w + \frac{1}{2}]$ | $1$ |
$5$ | $[5, 5, w - 3]$ | $-1$ |