Base field \(\Q(\sqrt{429}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 107\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 212x^{6} + 8308x^{4} - 62816x^{2} + 10816\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 11]$ | $-\frac{1}{14812}e^{6} + \frac{215}{14812}e^{4} - \frac{2106}{3703}e^{2} + \frac{6152}{3703}$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{14812}e^{6} - \frac{215}{14812}e^{4} + \frac{2106}{3703}e^{2} - \frac{2449}{3703}$ |
| 5 | $[5, 5, w + 1]$ | $-\frac{425}{3080896}e^{7} + \frac{22447}{770224}e^{5} - \frac{865955}{770224}e^{3} + \frac{112011}{14812}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{425}{3080896}e^{7} + \frac{22447}{770224}e^{5} - \frac{865955}{770224}e^{3} + \frac{112011}{14812}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 5]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 5]$ | $-\frac{425}{1540448}e^{7} + \frac{22447}{385112}e^{5} - \frac{865955}{385112}e^{3} + \frac{112011}{7406}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{425}{1540448}e^{7} + \frac{22447}{385112}e^{5} - \frac{865955}{385112}e^{3} + \frac{119417}{7406}e$ |
| 17 | $[17, 17, w - 10]$ | $\phantom{-}\frac{5}{16928}e^{6} - \frac{1749}{29624}e^{4} + \frac{54137}{29624}e^{2} - \frac{44837}{7406}$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{5}{16928}e^{6} - \frac{1749}{29624}e^{4} + \frac{54137}{29624}e^{2} - \frac{44837}{7406}$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}\frac{17}{96278}e^{7} - \frac{2013}{55016}e^{5} + \frac{250973}{192556}e^{3} - \frac{26385}{3703}e$ |
| 19 | $[19, 19, w + 15]$ | $\phantom{-}\frac{17}{96278}e^{7} - \frac{2013}{55016}e^{5} + \frac{250973}{192556}e^{3} - \frac{26385}{3703}e$ |
| 29 | $[29, 29, -2w + 21]$ | $-\frac{5}{16928}e^{6} + \frac{1749}{29624}e^{4} - \frac{54137}{29624}e^{2} + \frac{44837}{7406}$ |
| 29 | $[29, 29, 5w - 54]$ | $-\frac{5}{16928}e^{6} + \frac{1749}{29624}e^{4} - \frac{54137}{29624}e^{2} + \frac{44837}{7406}$ |
| 47 | $[47, 47, w + 18]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 28]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w + 27]$ | $\phantom{-}\frac{331}{770224}e^{7} - \frac{70107}{770224}e^{5} + \frac{1371425}{385112}e^{3} - \frac{28413}{1058}e$ |
| 59 | $[59, 59, w + 31]$ | $\phantom{-}\frac{331}{770224}e^{7} - \frac{70107}{770224}e^{5} + \frac{1371425}{385112}e^{3} - \frac{28413}{1058}e$ |
| 71 | $[71, 71, w + 21]$ | $-\frac{237}{1540448}e^{7} + \frac{25213}{770224}e^{5} - \frac{36105}{27508}e^{3} + \frac{43440}{3703}e$ |
| 71 | $[71, 71, w + 49]$ | $-\frac{237}{1540448}e^{7} + \frac{25213}{770224}e^{5} - \frac{36105}{27508}e^{3} + \frac{43440}{3703}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).