Base field 3.3.1129.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 31x^{12} + 380x^{10} - 2329x^{8} + 7373x^{6} - 10939x^{4} + 5378x^{2} - 676\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{50}{631}e^{12} + \frac{1340}{631}e^{10} - \frac{13372}{631}e^{8} + \frac{60540}{631}e^{6} - \frac{118799}{631}e^{4} + \frac{73108}{631}e^{2} - \frac{12074}{631}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{589}{16406}e^{13} - \frac{15659}{16406}e^{11} + \frac{77070}{8203}e^{9} - \frac{676437}{16406}e^{7} + \frac{1211023}{16406}e^{5} - \frac{478801}{16406}e^{3} + \frac{19336}{8203}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $\phantom{-}\frac{122}{8203}e^{13} - \frac{3522}{8203}e^{11} + \frac{39392}{8203}e^{9} - \frac{212963}{8203}e^{7} + \frac{560089}{8203}e^{5} - \frac{615086}{8203}e^{3} + \frac{179159}{8203}e$ |
| 13 | $[13, 13, w^{2} - w - 7]$ | $-\frac{402}{8203}e^{13} + \frac{10395}{8203}e^{11} - \frac{99005}{8203}e^{9} + \frac{417584}{8203}e^{7} - \frac{708953}{8203}e^{5} + \frac{218199}{8203}e^{3} + \frac{95481}{8203}e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{264}{8203}e^{13} + \frac{6949}{8203}e^{11} - \frac{67222}{8203}e^{9} + \frac{282927}{8203}e^{7} - \frac{434728}{8203}e^{5} - \frac{45619}{8203}e^{3} + \frac{162854}{8203}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{50}{631}e^{12} - \frac{1340}{631}e^{10} + \frac{13372}{631}e^{8} - \frac{59909}{631}e^{6} + \frac{110596}{631}e^{4} - \frac{47237}{631}e^{2} + \frac{3240}{631}$ |
| 29 | $[29, 29, 2w^{2} - 2w - 11]$ | $-\frac{93}{16406}e^{13} + \frac{1609}{16406}e^{11} - \frac{2239}{8203}e^{9} - \frac{62435}{16406}e^{7} + \frac{459845}{16406}e^{5} - \frac{969203}{16406}e^{3} + \frac{175686}{8203}e$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1889}{16406}e^{13} - \frac{50499}{16406}e^{11} + \frac{250906}{8203}e^{9} - \frac{2250477}{16406}e^{7} + \frac{4299797}{16406}e^{5} - \frac{2363203}{16406}e^{3} + \frac{135283}{8203}e$ |
| 37 | $[37, 37, -2w^{2} + 3w + 7]$ | $\phantom{-}\frac{463}{8203}e^{13} - \frac{12156}{8203}e^{11} + \frac{118701}{8203}e^{9} - \frac{528167}{8203}e^{7} + \frac{1050520}{8203}e^{5} - \frac{788238}{8203}e^{3} + \frac{285305}{8203}e$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-\frac{991}{8203}e^{13} + \frac{26054}{8203}e^{11} - \frac{253145}{8203}e^{9} + \frac{1094021}{8203}e^{7} - \frac{1919976}{8203}e^{5} + \frac{705203}{8203}e^{3} - \frac{612}{8203}e$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $-\frac{59}{631}e^{12} + \frac{1455}{631}e^{10} - \frac{13154}{631}e^{8} + \frac{52381}{631}e^{6} - \frac{83885}{631}e^{4} + \frac{28064}{631}e^{2} + \frac{720}{631}$ |
| 61 | $[61, 61, w^{2} + w - 10]$ | $-\frac{90}{631}e^{12} + \frac{2412}{631}e^{10} - \frac{24322}{631}e^{8} + \frac{112758}{631}e^{6} - \frac{230118}{631}e^{4} + \frac{150272}{631}e^{2} - \frac{20976}{631}$ |
| 67 | $[67, 67, 2w^{2} - w - 11]$ | $-\frac{1142}{8203}e^{13} + \frac{31489}{8203}e^{11} - \frac{327451}{8203}e^{9} + \frac{1582382}{8203}e^{7} - \frac{3499999}{8203}e^{5} + \frac{2896375}{8203}e^{3} - \frac{669287}{8203}e$ |
| 73 | $[73, 73, -w^{2} - 1]$ | $\phantom{-}\frac{139}{631}e^{12} - \frac{3599}{631}e^{10} + \frac{34423}{631}e^{8} - \frac{146721}{631}e^{6} + \frac{257305}{631}e^{4} - \frac{107303}{631}e^{2} + \frac{9512}{631}$ |
| 83 | $[83, 83, w^{2} - w - 10]$ | $\phantom{-}\frac{159}{631}e^{12} - \frac{4135}{631}e^{10} + \frac{39898}{631}e^{8} - \frac{173461}{631}e^{6} + \frac{321483}{631}e^{4} - \frac{174280}{631}e^{2} + \frac{22166}{631}$ |
| 89 | $[89, 89, -w^{2} + 4w - 2]$ | $-\frac{15}{631}e^{12} + \frac{402}{631}e^{10} - \frac{4264}{631}e^{8} + \frac{21948}{631}e^{6} - \frac{52235}{631}e^{4} + \frac{44396}{631}e^{2} - \frac{9806}{631}$ |
| 97 | $[97, 97, w^{2} - 2w - 7]$ | $-\frac{215}{16406}e^{13} + \frac{5131}{16406}e^{11} - \frac{21935}{8203}e^{9} + \frac{158731}{16406}e^{7} - \frac{206883}{16406}e^{5} - \frac{9591}{16406}e^{3} + \frac{16381}{8203}e$ |
| 97 | $[97, 97, -w^{2} - 4w - 5]$ | $\phantom{-}\frac{110}{631}e^{12} - \frac{2948}{631}e^{10} + \frac{29166}{631}e^{8} - \frac{128771}{631}e^{6} + \frac{236244}{631}e^{4} - \frac{111241}{631}e^{2} + \frac{19748}{631}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |