Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -w - 8]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 25x^{10} + 208x^{8} + 675x^{6} + 937x^{4} + 486x^{2} + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{11}{2545}e^{11} + \frac{35}{509}e^{9} + \frac{3}{2545}e^{7} - \frac{1667}{509}e^{5} - \frac{21273}{2545}e^{3} - \frac{11804}{2545}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{11}{2545}e^{11} + \frac{35}{509}e^{9} + \frac{3}{2545}e^{7} - \frac{1667}{509}e^{5} - \frac{21273}{2545}e^{3} - \frac{11804}{2545}e$ |
| 5 | $[5, 5, -3w + 25]$ | $\phantom{-}\frac{667}{3563}e^{10} + \frac{2210}{509}e^{8} + \frac{110820}{3563}e^{6} + \frac{249628}{3563}e^{4} + \frac{164018}{3563}e^{2} - \frac{4401}{3563}$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{3804}{17815}e^{11} + \frac{2562}{509}e^{9} + \frac{664357}{17815}e^{7} + \frac{328847}{3563}e^{5} + \frac{1386873}{17815}e^{3} + \frac{245619}{17815}e$ |
| 11 | $[11, 11, w - 9]$ | $-\frac{1010}{3563}e^{10} - \frac{3406}{509}e^{8} - \frac{176991}{3563}e^{6} - \frac{437046}{3563}e^{4} - \frac{342203}{3563}e^{2} - \frac{11685}{3563}$ |
| 11 | $[11, 11, -w - 9]$ | $\phantom{-}\frac{1226}{3563}e^{10} + \frac{4082}{509}e^{8} + \frac{206757}{3563}e^{6} + \frac{479707}{3563}e^{4} + \frac{348198}{3563}e^{2} + \frac{26531}{3563}$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{222}{2545}e^{11} + \frac{984}{509}e^{9} + \frac{31526}{2545}e^{7} + \frac{8789}{509}e^{5} - \frac{38786}{2545}e^{3} - \frac{71413}{2545}e$ |
| 17 | $[17, 17, w + 11]$ | $-\frac{870}{3563}e^{11} - \frac{2949}{509}e^{9} - \frac{154927}{3563}e^{7} - \frac{396397}{3563}e^{5} - \frac{360949}{3563}e^{3} - \frac{78997}{3563}e$ |
| 23 | $[23, 23, w + 1]$ | $-\frac{4422}{17815}e^{11} - \frac{3028}{509}e^{9} - \frac{813061}{17815}e^{7} - \frac{441522}{3563}e^{5} - \frac{2292499}{17815}e^{3} - \frac{690912}{17815}e$ |
| 23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{756}{2545}e^{11} + \frac{3516}{509}e^{9} + \frac{126068}{2545}e^{7} + \frac{55669}{509}e^{5} + \frac{133217}{2545}e^{3} - \frac{75289}{2545}e$ |
| 31 | $[31, 31, 4w - 33]$ | $\phantom{-}\frac{3342}{3563}e^{10} + \frac{11251}{509}e^{8} + \frac{582282}{3563}e^{6} + \frac{1424225}{3563}e^{4} + \frac{1122364}{3563}e^{2} + \frac{85795}{3563}$ |
| 31 | $[31, 31, 4w + 33]$ | $-\frac{89}{509}e^{10} - \frac{2110}{509}e^{8} - \frac{15757}{509}e^{6} - \frac{39406}{509}e^{4} - \frac{32824}{509}e^{2} - \frac{5462}{509}$ |
| 37 | $[37, 37, w + 12]$ | $-\frac{6368}{17815}e^{11} - \frac{4329}{509}e^{9} - \frac{1143979}{17815}e^{7} - \frac{593933}{3563}e^{5} - \frac{2754506}{17815}e^{3} - \frac{648163}{17815}e$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{7541}{17815}e^{11} - \frac{5001}{509}e^{9} - \frac{1251883}{17815}e^{7} - \frac{552212}{3563}e^{5} - \frac{1417732}{17815}e^{3} + \frac{699879}{17815}e$ |
| 53 | $[53, 53, w + 21]$ | $-\frac{22378}{17815}e^{11} - \frac{15123}{509}e^{9} - \frac{3945069}{17815}e^{7} - \frac{1973946}{3563}e^{5} - \frac{8228461}{17815}e^{3} - \frac{1039583}{17815}e$ |
| 53 | $[53, 53, w + 32]$ | $-\frac{10711}{17815}e^{11} - \frac{7136}{509}e^{9} - \frac{1808483}{17815}e^{7} - \frac{841097}{3563}e^{5} - \frac{3099002}{17815}e^{3} - \frac{279756}{17815}e$ |
| 61 | $[61, 61, -w - 3]$ | $-\frac{248}{3563}e^{10} - \frac{795}{509}e^{8} - \frac{36947}{3563}e^{6} - \frac{67324}{3563}e^{4} - \frac{46604}{3563}e^{2} - \frac{29186}{3563}$ |
| 61 | $[61, 61, w - 3]$ | $-\frac{388}{3563}e^{10} - \frac{1252}{509}e^{8} - \frac{59011}{3563}e^{6} - \frac{107973}{3563}e^{4} - \frac{34984}{3563}e^{2} - \frac{1067}{3563}$ |
| 73 | $[73, 73, w + 17]$ | $\phantom{-}\frac{24302}{17815}e^{11} + \frac{16414}{509}e^{9} + \frac{4281071}{17815}e^{7} + \frac{2151069}{3563}e^{5} + \frac{9353994}{17815}e^{3} + \frac{1689777}{17815}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{11}{2545}e^{11} - \frac{35}{509}e^{9} - \frac{3}{2545}e^{7} + \frac{1667}{509}e^{5} + \frac{21273}{2545}e^{3} + \frac{11804}{2545}e$ |
| $3$ | $[3, 3, w + 2]$ | $-\frac{11}{2545}e^{11} - \frac{35}{509}e^{9} - \frac{3}{2545}e^{7} + \frac{1667}{509}e^{5} + \frac{21273}{2545}e^{3} + \frac{11804}{2545}e$ |