Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{2} - w - 5]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 4x^{15} - 12x^{14} - 60x^{13} + 47x^{12} + 354x^{11} - 44x^{10} - 1052x^{9} - 145x^{8} + 1666x^{7} + 405x^{6} - 1358x^{5} - 384x^{4} + 500x^{3} + 144x^{2} - 56x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $-\frac{37}{122}e^{15} - \frac{55}{61}e^{14} + \frac{262}{61}e^{13} + \frac{803}{61}e^{12} - \frac{2907}{122}e^{11} - \frac{4527}{61}e^{10} + \frac{4123}{61}e^{9} + \frac{12443}{61}e^{8} - \frac{13233}{122}e^{7} - \frac{17164}{61}e^{6} + \frac{12565}{122}e^{5} + \frac{10866}{61}e^{4} - 56e^{3} - \frac{2662}{61}e^{2} + \frac{858}{61}e + \frac{290}{61}$ |
| 7 | $[7, 7, -w - 1]$ | $-\frac{15}{61}e^{15} - \frac{38}{61}e^{14} + \frac{252}{61}e^{13} + \frac{628}{61}e^{12} - \frac{1683}{61}e^{11} - \frac{4086}{61}e^{10} + \frac{5689}{61}e^{9} + \frac{13284}{61}e^{8} - \frac{10220}{61}e^{7} - \frac{22587}{61}e^{6} + \frac{9265}{61}e^{5} + \frac{19083}{61}e^{4} - 56e^{3} - \frac{6646}{61}e^{2} + \frac{178}{61}e + \frac{400}{61}$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{107}{122}e^{15} + \frac{164}{61}e^{14} - \frac{789}{61}e^{13} - \frac{2492}{61}e^{12} + \frac{9297}{122}e^{11} + \frac{14793}{61}e^{10} - \frac{14388}{61}e^{9} - \frac{43500}{61}e^{8} + \frac{51695}{122}e^{7} + \frac{65841}{61}e^{6} - \frac{54297}{122}e^{5} - \frac{47829}{61}e^{4} + 238e^{3} + \frac{13574}{61}e^{2} - \frac{2656}{61}e - \frac{776}{61}$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $-\frac{9}{61}e^{15} - \frac{35}{61}e^{14} + \frac{139}{61}e^{13} + \frac{572}{61}e^{12} - \frac{900}{61}e^{11} - \frac{3696}{61}e^{10} + \frac{3267}{61}e^{9} + \frac{11911}{61}e^{8} - \frac{7169}{61}e^{7} - \frac{19640}{61}e^{6} + \frac{8731}{61}e^{5} + \frac{14939}{61}e^{4} - 72e^{3} - \frac{3768}{61}e^{2} + \frac{424}{61}e - \frac{126}{61}$ |
| 23 | $[23, 23, -w - 3]$ | $\phantom{-}\frac{9}{61}e^{15} + \frac{35}{61}e^{14} - \frac{78}{61}e^{13} - \frac{450}{61}e^{12} - \frac{15}{61}e^{11} + \frac{2110}{61}e^{10} + \frac{2162}{61}e^{9} - \frac{4408}{61}e^{8} - \frac{8935}{61}e^{7} + \frac{3963}{61}e^{6} + \frac{15425}{61}e^{5} - \frac{1214}{61}e^{4} - 186e^{3} - \frac{14}{61}e^{2} + \frac{2504}{61}e + \frac{126}{61}$ |
| 23 | $[23, 23, w - 3]$ | $-\frac{57}{122}e^{15} - \frac{121}{61}e^{14} + \frac{247}{61}e^{13} + \frac{1608}{61}e^{12} - \frac{27}{122}e^{11} - \frac{7861}{61}e^{10} - \frac{5789}{61}e^{9} + \frac{17151}{61}e^{8} + \frac{43819}{122}e^{7} - \frac{15203}{61}e^{6} - \frac{65321}{122}e^{5} + \frac{1506}{61}e^{4} + 326e^{3} + \frac{3318}{61}e^{2} - \frac{3578}{61}e - \frac{582}{61}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}\frac{8}{61}e^{15} + \frac{4}{61}e^{14} - \frac{171}{61}e^{13} - \frac{95}{61}e^{12} + \frac{1410}{61}e^{11} + \frac{825}{61}e^{10} - \frac{5710}{61}e^{9} - \frac{3437}{61}e^{8} + \frac{11876}{61}e^{7} + \frac{7386}{61}e^{6} - \frac{11997}{61}e^{5} - \frac{8067}{61}e^{4} + 82e^{3} + \frac{4000}{61}e^{2} - \frac{648}{61}e - \frac{620}{61}$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $\phantom{-}\frac{105}{122}e^{15} + \frac{194}{61}e^{14} - \frac{699}{61}e^{13} - \frac{2930}{61}e^{12} + \frac{7145}{122}e^{11} + \frac{17351}{61}e^{10} - \frac{9389}{61}e^{9} - \frac{51252}{61}e^{8} + \frac{30853}{122}e^{7} + \frac{78719}{61}e^{6} - \frac{36185}{122}e^{5} - \frac{58647}{61}e^{4} + 201e^{3} + \frac{17100}{61}e^{2} - \frac{2758}{61}e - \frac{1034}{61}$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $-\frac{113}{122}e^{15} - \frac{196}{61}e^{14} + \frac{815}{61}e^{13} + \frac{3008}{61}e^{12} - \frac{9653}{122}e^{11} - \frac{18221}{61}e^{10} + \frac{16026}{61}e^{9} + \frac{55502}{61}e^{8} - \frac{67495}{122}e^{7} - \frac{88817}{61}e^{6} + \frac{86917}{122}e^{5} + \frac{70397}{61}e^{4} - 449e^{3} - \frac{23492}{61}e^{2} + \frac{5522}{61}e + \frac{1710}{61}$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{16}{61}e^{15} - \frac{8}{61}e^{14} + \frac{342}{61}e^{13} + \frac{190}{61}e^{12} - \frac{2820}{61}e^{11} - \frac{1650}{61}e^{10} + \frac{11481}{61}e^{9} + \frac{6874}{61}e^{8} - \frac{24545}{61}e^{7} - \frac{14589}{61}e^{6} + \frac{27410}{61}e^{5} + \frac{14731}{61}e^{4} - 252e^{3} - \frac{5316}{61}e^{2} + \frac{3492}{61}e + \frac{264}{61}$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $-\frac{97}{61}e^{15} - \frac{323}{61}e^{14} + \frac{1471}{61}e^{13} + \frac{5094}{61}e^{12} - \frac{9151}{61}e^{11} - \frac{31742}{61}e^{10} + \frac{31063}{61}e^{9} + \frac{99128}{61}e^{8} - \frac{63263}{61}e^{7} - \frac{160910}{61}e^{6} + \frac{75123}{61}e^{5} + \frac{126185}{61}e^{4} - 708e^{3} - \frac{39106}{61}e^{2} + \frac{7918}{61}e + \frac{2424}{61}$ |
| 71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $-\frac{86}{61}e^{15} - \frac{226}{61}e^{14} + \frac{1396}{61}e^{13} + \frac{3568}{61}e^{12} - \frac{9271}{61}e^{11} - \frac{22304}{61}e^{10} + \frac{32743}{61}e^{9} + \frac{70391}{61}e^{8} - \frac{65935}{61}e^{7} - \frac{117555}{61}e^{6} + \frac{73168}{61}e^{5} + \frac{98051}{61}e^{4} - 616e^{3} - \frac{33362}{61}e^{2} + \frac{5258}{61}e + \frac{1968}{61}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $\phantom{-}\frac{49}{61}e^{15} + \frac{55}{61}e^{14} - \frac{1116}{61}e^{13} - \frac{1291}{61}e^{12} + \frac{9719}{61}e^{11} + \frac{10871}{61}e^{10} - \frac{42004}{61}e^{9} - \frac{42821}{61}e^{8} + \frac{96317}{61}e^{7} + \frac{83349}{61}e^{6} - \frac{113673}{61}e^{5} - \frac{75953}{61}e^{4} + 968e^{3} + \frac{26940}{61}e^{2} - \frac{8544}{61}e - \frac{1510}{61}$ |
| 73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $-\frac{151}{122}e^{15} - \frac{297}{61}e^{14} + \frac{878}{61}e^{13} + \frac{4263}{61}e^{12} - \frac{6743}{122}e^{11} - \frac{23604}{61}e^{10} + \frac{4013}{61}e^{9} + \frac{63703}{61}e^{8} + \frac{6085}{122}e^{7} - \frac{85878}{61}e^{6} - \frac{17061}{122}e^{5} + \frac{51027}{61}e^{4} + 69e^{3} - \frac{8348}{61}e^{2} - \frac{198}{61}e - \frac{508}{61}$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{63}{61}e^{15} + \frac{306}{61}e^{14} - \frac{546}{61}e^{13} - \frac{4309}{61}e^{12} + \frac{200}{61}e^{11} + \frac{23310}{61}e^{10} + \frac{10559}{61}e^{9} - \frac{61356}{61}e^{8} - \frac{37779}{61}e^{7} + \frac{81177}{61}e^{6} + \frac{50208}{61}e^{5} - \frac{48819}{61}e^{4} - 426e^{3} + \frac{9418}{61}e^{2} + \frac{3864}{61}e + \frac{28}{61}$ |
| 79 | $[79, 79, -2w^{3} + 8w + 5]$ | $-\frac{63}{61}e^{15} - \frac{245}{61}e^{14} + \frac{729}{61}e^{13} + \frac{3455}{61}e^{12} - \frac{2884}{61}e^{11} - \frac{18796}{61}e^{10} + \frac{4569}{61}e^{9} + \frac{50376}{61}e^{8} - \frac{3396}{61}e^{7} - \frac{70380}{61}e^{6} + \frac{5180}{61}e^{5} + \frac{49795}{61}e^{4} - 122e^{3} - \frac{15762}{61}e^{2} + \frac{2724}{61}e + \frac{1192}{61}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{116}{61}e^{15} + \frac{363}{61}e^{14} - \frac{1656}{61}e^{13} - \frac{5373}{61}e^{12} + \frac{9465}{61}e^{11} + \frac{30964}{61}e^{10} - \frac{28871}{61}e^{9} - \frac{88175}{61}e^{8} + \frac{52642}{61}e^{7} + \frac{128874}{61}e^{6} - \frac{57111}{61}e^{5} - \frac{89796}{61}e^{4} + 500e^{3} + \frac{24572}{61}e^{2} - \frac{5492}{61}e - \frac{1670}{61}$ |
| 89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $-\frac{173}{122}e^{15} - \frac{333}{61}e^{14} + \frac{1197}{61}e^{13} + \frac{5179}{61}e^{12} - \frac{13213}{122}e^{11} - \frac{31822}{61}e^{10} + \frac{19962}{61}e^{9} + \frac{98296}{61}e^{8} - \frac{78241}{122}e^{7} - \frac{159245}{61}e^{6} + \frac{100309}{122}e^{5} + \frac{127107}{61}e^{4} - 531e^{3} - \frac{41664}{61}e^{2} + \frac{6122}{61}e + \frac{3120}{61}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,w^{2}-w-5]$ | $-1$ |