Base field 6.6.905177.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 9x^{3} + 7x^{2} - 9x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[43, 43, -w^{2} - w + 2]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 15x^{8} + 67x^{7} + 15x^{6} - 766x^{5} + 1002x^{4} + 2479x^{3} - 3597x^{2} - 3157x + 1123\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, -2w^{5} - w^{4} + 13w^{3} + w^{2} - 16w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -3w^{5} - w^{4} + 19w^{3} - 2w^{2} - 20w + 1]$ | $-\frac{8071}{9692}e^{8} + \frac{88479}{9692}e^{7} - \frac{91765}{4846}e^{6} - \frac{215652}{2423}e^{5} + \frac{1352257}{4846}e^{4} + \frac{1414575}{4846}e^{3} - \frac{8641843}{9692}e^{2} - \frac{5794985}{9692}e + \frac{1139861}{4846}$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}\frac{10369}{9692}e^{8} - \frac{28306}{2423}e^{7} + \frac{232183}{9692}e^{6} + \frac{277335}{2423}e^{5} - \frac{1717633}{4846}e^{4} - \frac{915186}{2423}e^{3} + \frac{10973559}{9692}e^{2} + \frac{1855931}{2423}e - \frac{2877821}{9692}$ |
| 29 | $[29, 29, -w^{5} - w^{4} + 5w^{3} + 2w^{2} - 3w - 1]$ | $\phantom{-}\frac{7091}{4846}e^{8} - \frac{38747}{2423}e^{7} + \frac{159747}{4846}e^{6} + \frac{377732}{2423}e^{5} - \frac{1178169}{2423}e^{4} - \frac{1234345}{2423}e^{3} + \frac{7516011}{4846}e^{2} + \frac{2502450}{2423}e - \frac{1960671}{4846}$ |
| 41 | $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$ | $\phantom{-}\frac{543}{9692}e^{8} - \frac{2419}{4846}e^{7} + \frac{3775}{9692}e^{6} + \frac{14629}{2423}e^{5} - \frac{44765}{4846}e^{4} - \frac{56174}{2423}e^{3} + \frac{282773}{9692}e^{2} + \frac{141937}{4846}e - \frac{67817}{9692}$ |
| 41 | $[41, 41, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 5]$ | $\phantom{-}\frac{7363}{4846}e^{8} - \frac{40222}{2423}e^{7} + \frac{165181}{4846}e^{6} + \frac{394213}{2423}e^{5} - \frac{1223194}{2423}e^{4} - \frac{1299895}{2423}e^{3} + \frac{7830445}{4846}e^{2} + \frac{2633852}{2423}e - \frac{2077845}{4846}$ |
| 43 | $[43, 43, -w^{2} - w + 2]$ | $\phantom{-}1$ |
| 43 | $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 5]$ | $\phantom{-}\frac{641}{4846}e^{8} - \frac{3574}{2423}e^{7} + \frac{15603}{4846}e^{6} + \frac{33646}{2423}e^{5} - \frac{111603}{2423}e^{4} - \frac{103718}{2423}e^{3} + \frac{704531}{4846}e^{2} + \frac{208700}{2423}e - \frac{187677}{4846}$ |
| 43 | $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$ | $-\frac{1663}{2423}e^{8} + \frac{35823}{4846}e^{7} - \frac{71257}{4846}e^{6} - \frac{175428}{2423}e^{5} + \frac{527598}{2423}e^{4} + \frac{572960}{2423}e^{3} - \frac{1666012}{2423}e^{2} - \frac{2229315}{4846}e + \frac{902623}{4846}$ |
| 43 | $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 15w + 3]$ | $\phantom{-}\frac{1959}{9692}e^{8} - \frac{5227}{2423}e^{7} + \frac{40473}{9692}e^{6} + \frac{51720}{2423}e^{5} - \frac{302891}{4846}e^{4} - \frac{170854}{2423}e^{3} + \frac{1915261}{9692}e^{2} + \frac{329763}{2423}e - \frac{481263}{9692}$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 6w^{3} + 3w^{2} - 7w]$ | $\phantom{-}\frac{659}{4846}e^{8} - \frac{3440}{2423}e^{7} + \frac{12435}{4846}e^{6} + \frac{34897}{2423}e^{5} - \frac{95644}{2423}e^{4} - \frac{118995}{2423}e^{3} + \frac{605365}{4846}e^{2} + \frac{227836}{2423}e - \frac{161331}{4846}$ |
| 71 | $[71, 71, -5w^{5} - 2w^{4} + 32w^{3} - w^{2} - 35w - 2]$ | $-\frac{31539}{9692}e^{8} + \frac{85733}{2423}e^{7} - \frac{698053}{9692}e^{6} - \frac{837325}{2423}e^{5} + \frac{5152717}{4846}e^{4} + \frac{2739888}{2423}e^{3} - \frac{32731085}{9692}e^{2} - \frac{5480012}{2423}e + \frac{8650523}{9692}$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 6]$ | $-\frac{6019}{2423}e^{8} + \frac{65725}{2423}e^{7} - \frac{135195}{2423}e^{6} - \frac{640378}{2423}e^{5} + \frac{1991458}{2423}e^{4} + \frac{2088830}{2423}e^{3} - \frac{6329507}{2423}e^{2} - \frac{4213581}{2423}e + \frac{1665627}{2423}$ |
| 71 | $[71, 71, -3w^{5} - 2w^{4} + 19w^{3} + 5w^{2} - 22w - 7]$ | $\phantom{-}\frac{10611}{2423}e^{8} - \frac{115813}{2423}e^{7} + \frac{238051}{2423}e^{6} + \frac{1128440}{2423}e^{5} - \frac{3507438}{2423}e^{4} - \frac{3684384}{2423}e^{3} + \frac{11149587}{2423}e^{2} + \frac{7453939}{2423}e - \frac{2874141}{2423}$ |
| 71 | $[71, 71, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 6]$ | $\phantom{-}\frac{8409}{9692}e^{8} - \frac{45627}{4846}e^{7} + \frac{184617}{9692}e^{6} + \frac{223763}{2423}e^{5} - \frac{1369457}{4846}e^{4} - \frac{734956}{2423}e^{3} + \frac{8721895}{9692}e^{2} + \frac{2931469}{4846}e - \frac{2317255}{9692}$ |
| 83 | $[83, 83, -2w^{5} - w^{4} + 12w^{3} - 12w + 1]$ | $-\frac{27793}{9692}e^{8} + \frac{152239}{4846}e^{7} - \frac{630449}{9692}e^{6} - \frac{742285}{2423}e^{5} + \frac{4645353}{4846}e^{4} + \frac{2431056}{2423}e^{3} - \frac{29627539}{9692}e^{2} - \frac{9890325}{4846}e + \frac{7638163}{9692}$ |
| 83 | $[83, 83, -2w^{5} - w^{4} + 13w^{3} - 16w + 1]$ | $-\frac{32961}{9692}e^{8} + \frac{90132}{2423}e^{7} - \frac{743387}{9692}e^{6} - \frac{880682}{2423}e^{5} + \frac{5488713}{4846}e^{4} + \frac{2893863}{2423}e^{3} - \frac{35044495}{9692}e^{2} - \frac{5899087}{2423}e + \frac{9098801}{9692}$ |
| 83 | $[83, 83, -4w^{5} - 2w^{4} + 26w^{3} + 3w^{2} - 29w - 6]$ | $-\frac{24619}{9692}e^{8} + \frac{133869}{4846}e^{7} - \frac{544555}{9692}e^{6} - \frac{655007}{2423}e^{5} + \frac{4027681}{4846}e^{4} + \frac{2145004}{2423}e^{3} - \frac{25600801}{9692}e^{2} - \frac{8559407}{4846}e + \frac{6652789}{9692}$ |
| 83 | $[83, 83, 2w^{5} - 13w^{3} + 5w^{2} + 13w - 1]$ | $\phantom{-}\frac{50319}{9692}e^{8} - \frac{274767}{4846}e^{7} + \frac{1129039}{9692}e^{6} + \frac{1342127}{2423}e^{5} - \frac{8330377}{4846}e^{4} - \frac{4408782}{2423}e^{3} + \frac{53070269}{9692}e^{2} + \frac{17874165}{4846}e - \frac{13781289}{9692}$ |
| 97 | $[97, 97, -3w^{5} + 20w^{3} - 8w^{2} - 22w + 5]$ | $-\frac{10529}{2423}e^{8} + \frac{229491}{4846}e^{7} - \frac{468621}{4846}e^{6} - \frac{1124311}{2423}e^{5} + \frac{3468425}{2423}e^{4} + \frac{3700804}{2423}e^{3} - \frac{11055899}{2423}e^{2} - \frac{14906205}{4846}e + \frac{5766215}{4846}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $43$ | $[43,43,-w^{2}-w+2]$ | $-1$ |