Base field 4.4.12400.1
Generator \(w\), with minimal polynomial \(x^{4} - 12x^{2} + 31\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9,3,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{9}{2}]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{11}{2}]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w - 4]$ | $\phantom{-}0$ |
5 | $[5, 5, -\frac{1}{2}w^{2} - w + \frac{3}{2}]$ | $\phantom{-}0$ |
9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - \frac{9}{2}]$ | $-2$ |
9 | $[9, 3, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{7}{2}w + \frac{9}{2}]$ | $\phantom{-}1$ |
19 | $[19, 19, -\frac{1}{2}w^{2} + w + \frac{5}{2}]$ | $-2$ |
19 | $[19, 19, \frac{1}{2}w^{2} + w - \frac{5}{2}]$ | $-2$ |
29 | $[29, 29, -\frac{3}{2}w^{2} - w + \frac{17}{2}]$ | $\phantom{-}6$ |
29 | $[29, 29, -\frac{3}{2}w^{2} + w + \frac{17}{2}]$ | $-6$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-4$ |
59 | $[59, 59, \frac{1}{2}w^{2} + w - \frac{11}{2}]$ | $\phantom{-}12$ |
59 | $[59, 59, \frac{1}{2}w^{2} - w - \frac{11}{2}]$ | $\phantom{-}0$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 5]$ | $-8$ |
61 | $[61, 61, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}4$ |
71 | $[71, 71, -\frac{1}{2}w^{3} - 2w^{2} + \frac{11}{2}w + 13]$ | $-12$ |
71 | $[71, 71, \frac{3}{2}w^{3} + 2w^{2} - \frac{23}{2}w - 18]$ | $-12$ |
79 | $[79, 79, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{1}{2}]$ | $-16$ |
79 | $[79, 79, -2w^{2} + w + 10]$ | $\phantom{-}16$ |
79 | $[79, 79, 2w^{2} + w - 10]$ | $-8$ |
79 | $[79, 79, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + \frac{1}{2}]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9,3,\frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - \frac{9}{2}]$ | $-1$ |