Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[47, 47, w^{3} - w^{2} - 4w]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $31$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 8x^{10} + 4x^{9} - 105x^{8} - 224x^{7} + 129x^{6} + 446x^{5} - 98x^{4} - 210x^{3} + 8x^{2} + 28x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-\frac{1487}{522}e^{10} - \frac{3809}{174}e^{9} - \frac{1105}{261}e^{8} + \frac{157915}{522}e^{7} + \frac{284195}{522}e^{6} - \frac{293947}{522}e^{5} - \frac{603587}{522}e^{4} + \frac{5708}{9}e^{3} + \frac{124786}{261}e^{2} - \frac{39649}{261}e - \frac{13238}{261}$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $\phantom{-}\frac{745}{174}e^{10} + \frac{955}{29}e^{9} + \frac{602}{87}e^{8} - \frac{78731}{174}e^{7} - \frac{71486}{87}e^{6} + \frac{141803}{174}e^{5} + \frac{147608}{87}e^{4} - \frac{2821}{3}e^{3} - \frac{59201}{87}e^{2} + \frac{20402}{87}e + \frac{6154}{87}$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $\phantom{-}\frac{2252}{261}e^{10} + \frac{5831}{87}e^{9} + \frac{4937}{261}e^{8} - \frac{237628}{261}e^{7} - \frac{449093}{261}e^{6} + \frac{395143}{261}e^{5} + \frac{911675}{261}e^{4} - \frac{14944}{9}e^{3} - \frac{370550}{261}e^{2} + \frac{103283}{261}e + \frac{37636}{261}$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $\phantom{-}\frac{36}{29}e^{10} + \frac{280}{29}e^{9} + \frac{85}{29}e^{8} - \frac{3786}{29}e^{7} - \frac{7271}{29}e^{6} + \frac{6060}{29}e^{5} + \frac{14835}{29}e^{4} - 216e^{3} - \frac{6226}{29}e^{2} + \frac{1591}{29}e + \frac{532}{29}$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $\phantom{-}\frac{206}{29}e^{10} + \frac{1599}{29}e^{9} + \frac{430}{29}e^{8} - \frac{21819}{29}e^{7} - \frac{40928}{29}e^{6} + \frac{37364}{29}e^{5} + \frac{84749}{29}e^{4} - 1401e^{3} - \frac{35401}{29}e^{2} + \frac{9618}{29}e + \frac{3650}{29}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $\phantom{-}1$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $-\frac{3757}{174}e^{10} - \frac{9735}{58}e^{9} - \frac{4211}{87}e^{8} + \frac{396305}{174}e^{7} + \frac{751699}{174}e^{6} - \frac{653753}{174}e^{5} - \frac{1524289}{174}e^{4} + \frac{12277}{3}e^{3} + \frac{309254}{87}e^{2} - \frac{85823}{87}e - \frac{31174}{87}$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $-\frac{4355}{261}e^{10} - \frac{11309}{87}e^{9} - \frac{10451}{261}e^{8} + \frac{458257}{261}e^{7} + \frac{878309}{261}e^{6} - \frac{731719}{261}e^{5} - \frac{1750787}{261}e^{4} + \frac{27448}{9}e^{3} + \frac{693512}{261}e^{2} - \frac{189914}{261}e - \frac{68356}{261}$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $-\frac{2153}{261}e^{10} - \frac{5555}{87}e^{9} - \frac{4145}{261}e^{8} + \frac{228043}{261}e^{7} + \frac{422696}{261}e^{6} - \frac{399184}{261}e^{5} - \frac{874163}{261}e^{4} + \frac{15520}{9}e^{3} + \frac{362288}{261}e^{2} - \frac{112922}{261}e - \frac{37942}{261}$ |
| 64 | $[64, 2, -2]$ | $-\frac{66}{29}e^{10} - \frac{523}{29}e^{9} - \frac{238}{29}e^{8} + \frac{6854}{29}e^{7} + \frac{14263}{29}e^{6} - \frac{8413}{29}e^{5} - \frac{26574}{29}e^{4} + 266e^{3} + \frac{9742}{29}e^{2} - \frac{1694}{29}e - \frac{695}{29}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{949}{174}e^{10} + \frac{1213}{29}e^{9} + \frac{635}{87}e^{8} - \frac{100997}{174}e^{7} - \frac{89888}{87}e^{6} + \frac{193079}{174}e^{5} + \frac{193193}{87}e^{4} - \frac{3829}{3}e^{3} - \frac{82013}{87}e^{2} + \frac{28820}{87}e + \frac{9034}{87}$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $\phantom{-}\frac{9731}{522}e^{10} + \frac{12625}{87}e^{9} + \frac{11374}{261}e^{8} - \frac{1025083}{522}e^{7} - \frac{978049}{261}e^{6} + \frac{1659589}{522}e^{5} + \frac{1961164}{261}e^{4} - \frac{31304}{9}e^{3} - \frac{784999}{261}e^{2} + \frac{218614}{261}e + \frac{79082}{261}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{4369}{522}e^{10} + \frac{5627}{87}e^{9} + \frac{4136}{261}e^{8} - \frac{461189}{522}e^{7} - \frac{426836}{261}e^{6} + \frac{798359}{522}e^{5} + \frac{870842}{261}e^{4} - \frac{15547}{9}e^{3} - \frac{348023}{261}e^{2} + \frac{108728}{261}e + \frac{37204}{261}$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $-\frac{1921}{522}e^{10} - \frac{4975}{174}e^{9} - \frac{2174}{261}e^{8} + \frac{201827}{522}e^{7} + \frac{383053}{522}e^{6} - \frac{325553}{522}e^{5} - \frac{755437}{522}e^{4} + \frac{6223}{9}e^{3} + \frac{141878}{261}e^{2} - \frac{41903}{261}e - \frac{12562}{261}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $-\frac{6935}{522}e^{10} - \frac{9007}{87}e^{9} - \frac{8455}{261}e^{8} + \frac{729007}{522}e^{7} + \frac{700936}{261}e^{6} - \frac{1152157}{522}e^{5} - \frac{1394395}{261}e^{4} + \frac{21407}{9}e^{3} + \frac{552580}{261}e^{2} - \frac{147700}{261}e - \frac{54614}{261}$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $-\frac{2441}{174}e^{10} - \frac{6321}{58}e^{9} - \frac{2659}{87}e^{8} + \frac{257809}{174}e^{7} + \frac{486461}{174}e^{6} - \frac{431569}{174}e^{5} - \frac{989363}{174}e^{4} + \frac{8252}{3}e^{3} + \frac{202684}{87}e^{2} - \frac{58939}{87}e - \frac{21302}{87}$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $-\frac{653}{261}e^{10} - \frac{1679}{87}e^{9} - \frac{1106}{261}e^{8} + \frac{69307}{261}e^{7} + \frac{126311}{261}e^{6} - \frac{126094}{261}e^{5} - \frac{264245}{261}e^{4} + \frac{5086}{9}e^{3} + \frac{113756}{261}e^{2} - \frac{39854}{261}e - \frac{14422}{261}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $-\frac{323}{18}e^{10} - \frac{418}{3}e^{9} - \frac{352}{9}e^{8} + \frac{34069}{18}e^{7} + \frac{32170}{9}e^{6} - \frac{56701}{18}e^{5} - \frac{65245}{9}e^{4} + \frac{31399}{9}e^{3} + \frac{26653}{9}e^{2} - \frac{7864}{9}e - \frac{2804}{9}$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{13147}{522}e^{10} - \frac{16964}{87}e^{9} - \frac{13061}{261}e^{8} + \frac{1388663}{522}e^{7} + \frac{1293560}{261}e^{6} - \frac{2381375}{522}e^{5} - \frac{2644190}{261}e^{4} + \frac{45772}{9}e^{3} + \frac{1067003}{261}e^{2} - \frac{319892}{261}e - \frac{110116}{261}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47, 47, w^{3} - w^{2} - 4w]$ | $-1$ |