Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 13 x^2 + 14 x + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20,10,-\frac{2}{19} w^3 + \frac{3}{19} w^2 - \frac{1}{19} w - 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{2}{19} w^3 + \frac{3}{19} w^2 + \frac{37}{19} w - 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, \frac{3}{19} w^3 + \frac{5}{19} w^2 - \frac{27}{19} w - 1]$ | $-3$ |
| 5 | $[5, 5, -\frac{3}{19} w^3 + \frac{14}{19} w^2 + \frac{8}{19} w - 2]$ | $-1$ |
| 9 | $[9, 3, -\frac{2}{19} w^3 + \frac{3}{19} w^2 + \frac{37}{19} w - 4]$ | $\phantom{-}3$ |
| 19 | $[19, 19, -w]$ | $\phantom{-}1$ |
| 19 | $[19, 19, \frac{4}{19} w^3 - \frac{6}{19} w^2 - \frac{55}{19} w + 1]$ | $\phantom{-}1$ |
| 19 | $[19, 19, \frac{4}{19} w^3 - \frac{6}{19} w^2 - \frac{55}{19} w + 2]$ | $-2$ |
| 19 | $[19, 19, w - 1]$ | $-2$ |
| 29 | $[29, 29, -\frac{5}{19} w^3 - \frac{2}{19} w^2 + \frac{64}{19} w + 2]$ | $-9$ |
| 29 | $[29, 29, \frac{10}{19} w^3 - \frac{34}{19} w^2 - \frac{71}{19} w + 9]$ | $-9$ |
| 29 | $[29, 29, \frac{4}{19} w^3 - \frac{6}{19} w^2 - \frac{55}{19} w + 4]$ | $\phantom{-}6$ |
| 29 | $[29, 29, -w + 3]$ | $\phantom{-}6$ |
| 49 | $[49, 7, \frac{5}{19} w^3 - \frac{17}{19} w^2 - \frac{64}{19} w + 11]$ | $-8$ |
| 49 | $[49, 7, \frac{6}{19} w^3 - \frac{9}{19} w^2 - \frac{92}{19} w - 1]$ | $-8$ |
| 71 | $[71, 71, \frac{3}{19} w^3 + \frac{5}{19} w^2 - \frac{46}{19} w - 1]$ | $-3$ |
| 71 | $[71, 71, \frac{6}{19} w^3 - \frac{9}{19} w^2 - \frac{73}{19} w]$ | $-3$ |
| 71 | $[71, 71, \frac{6}{19} w^3 - \frac{9}{19} w^2 - \frac{73}{19} w + 4]$ | $\phantom{-}0$ |
| 71 | $[71, 71, -\frac{3}{19} w^3 + \frac{14}{19} w^2 + \frac{27}{19} w - 3]$ | $\phantom{-}0$ |
| 101 | $[101, 101, \frac{7}{19} w^3 - \frac{1}{19} w^2 - \frac{63}{19} w - 3]$ | $\phantom{-}0$ |
| 101 | $[101, 101, -\frac{9}{19} w^3 + \frac{23}{19} w^2 + \frac{81}{19} w - 5]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,\frac{2}{19} w^3 - \frac{3}{19} w^2 - \frac{37}{19} w - 1]$ | $-1$ |
| $5$ | $[5,5,-\frac{3}{19} w^3 + \frac{14}{19} w^2 + \frac{8}{19} w - 2]$ | $1$ |