Base field 6.6.1387029.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - x^{2} - 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[37,37,-w^{3} + 2w^{2} + 3w - 2]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} + 11x^{16} + 27x^{15} - 118x^{14} - 642x^{13} - 117x^{12} + 4264x^{11} + 5833x^{10} - 11153x^{9} - 27250x^{8} + 6873x^{7} + 52200x^{6} + 17038x^{5} - 41733x^{4} - 25278x^{3} + 9245x^{2} + 7057x + 331\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ | $\phantom{-}\frac{210970130}{104105517}e^{16} + \frac{616674100}{34701839}e^{15} + \frac{1581921917}{104105517}e^{14} - \frac{28328387411}{104105517}e^{13} - \frac{72283213603}{104105517}e^{12} + \frac{134878051649}{104105517}e^{11} + \frac{198869349188}{34701839}e^{10} - \frac{89074043950}{104105517}e^{9} - \frac{2133071886146}{104105517}e^{8} - \frac{1025627749529}{104105517}e^{7} + \frac{1218121856222}{34701839}e^{6} + \frac{2912336833499}{104105517}e^{5} - \frac{2747625252094}{104105517}e^{4} - \frac{901509917249}{34701839}e^{3} + \frac{576047490835}{104105517}e^{2} + \frac{665292828760}{104105517}e + \frac{32282431655}{104105517}$ |
| 25 | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ | $-\frac{7307064}{34701839}e^{16} - \frac{146129257}{69403678}e^{15} - \frac{240044189}{69403678}e^{14} + \frac{2026297545}{69403678}e^{13} + \frac{7337537929}{69403678}e^{12} - \frac{3344616656}{34701839}e^{11} - \frac{28493807498}{34701839}e^{10} - \frac{10754747083}{34701839}e^{9} + \frac{197474568171}{69403678}e^{8} + \frac{180849559371}{69403678}e^{7} - \frac{164656661772}{34701839}e^{6} - \frac{202665080035}{34701839}e^{5} + \frac{119677823668}{34701839}e^{4} + \frac{176247548257}{34701839}e^{3} - \frac{45978148277}{69403678}e^{2} - \frac{42360680881}{34701839}e - \frac{4468947701}{69403678}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{13136671}{34701839}e^{16} + \frac{806583187}{208211034}e^{15} + \frac{1445988599}{208211034}e^{14} - \frac{10894401799}{208211034}e^{13} - \frac{14044251687}{69403678}e^{12} + \frac{15841115828}{104105517}e^{11} + \frac{53882380359}{34701839}e^{10} + \frac{25778753722}{34701839}e^{9} - \frac{1111084670537}{208211034}e^{8} - \frac{1116729911207}{208211034}e^{7} + \frac{920855286683}{104105517}e^{6} + \frac{1215765927574}{104105517}e^{5} - \frac{670010553320}{104105517}e^{4} - \frac{1043780124617}{104105517}e^{3} + \frac{268423159903}{208211034}e^{2} + \frac{248440901954}{104105517}e + \frac{24330913471}{208211034}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}1$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ | $\phantom{-}\frac{14141587}{69403678}e^{16} + \frac{253210202}{104105517}e^{15} + \frac{1275672149}{208211034}e^{14} - \frac{3124925657}{104105517}e^{13} - \frac{5266217696}{34701839}e^{12} + \frac{4500547268}{104105517}e^{11} + \frac{39079072985}{34701839}e^{10} + \frac{57956036213}{69403678}e^{9} - \frac{396809311720}{104105517}e^{8} - \frac{481359425470}{104105517}e^{7} + \frac{651561160238}{104105517}e^{6} + \frac{986343704194}{104105517}e^{5} - \frac{470321536493}{104105517}e^{4} - \frac{1653346706587}{208211034}e^{3} + \frac{184784177341}{208211034}e^{2} + \frac{194379156449}{104105517}e + \frac{9152899640}{104105517}$ |
| 49 | $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ | $\phantom{-}\frac{70319119}{208211034}e^{16} + \frac{153533077}{69403678}e^{15} - \frac{588670307}{208211034}e^{14} - \frac{8827191571}{208211034}e^{13} - \frac{2122895257}{104105517}e^{12} + \frac{33256108169}{104105517}e^{11} + \frac{11009789853}{34701839}e^{10} - \frac{256109171795}{208211034}e^{9} - \frac{289975124413}{208211034}e^{8} + \frac{274932621898}{104105517}e^{7} + \frac{94333965001}{34701839}e^{6} - \frac{332067685237}{104105517}e^{5} - \frac{236169134491}{104105517}e^{4} + \frac{135639657433}{69403678}e^{3} + \frac{56267071660}{104105517}e^{2} - \frac{79283069599}{208211034}e - \frac{2558815285}{104105517}$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-\frac{464110484}{104105517}e^{16} - \frac{4021821914}{104105517}e^{15} - \frac{1039456173}{34701839}e^{14} + \frac{62231907241}{104105517}e^{13} + \frac{152686255273}{104105517}e^{12} - \frac{305251164289}{104105517}e^{11} - \frac{423736860012}{34701839}e^{10} + \frac{279259150099}{104105517}e^{9} + \frac{1522399041459}{34701839}e^{8} + \frac{644753428612}{34701839}e^{7} - \frac{7858799473871}{104105517}e^{6} - \frac{1940043224826}{34701839}e^{5} + \frac{1979128154750}{34701839}e^{4} + \frac{5481621077810}{104105517}e^{3} - \frac{418365682983}{34701839}e^{2} - \frac{452418829571}{34701839}e - \frac{65146123879}{104105517}$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{443565280}{104105517}e^{16} - \frac{3910213411}{104105517}e^{15} - \frac{1157177966}{34701839}e^{14} + \frac{59650351307}{104105517}e^{13} + \frac{154572721862}{104105517}e^{12} - \frac{280916355647}{104105517}e^{11} - \frac{423935012670}{34701839}e^{10} + \frac{158821978676}{104105517}e^{9} + \frac{1513373052607}{34701839}e^{8} + \frac{756092971715}{34701839}e^{7} - \frac{7768265361172}{104105517}e^{6} - \frac{2108885876118}{34701839}e^{5} + \frac{1944065613968}{34701839}e^{4} + \frac{5848132358824}{104105517}e^{3} - \frac{406260517989}{34701839}e^{2} - \frac{479255147319}{34701839}e - \frac{70298611397}{104105517}$ |
| 61 | $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ | $-\frac{563720765}{208211034}e^{16} - \frac{824680670}{34701839}e^{15} - \frac{2128163287}{104105517}e^{14} + \frac{37873274590}{104105517}e^{13} + \frac{193705353079}{208211034}e^{12} - \frac{180210666670}{104105517}e^{11} - \frac{266397710314}{34701839}e^{10} + \frac{236588652571}{208211034}e^{9} + \frac{2857839590023}{104105517}e^{8} + \frac{2745392236319}{208211034}e^{7} - \frac{1632729950720}{34701839}e^{6} - \frac{3892130921125}{104105517}e^{5} + \frac{3685209974216}{104105517}e^{4} + \frac{2406433604007}{69403678}e^{3} - \frac{1545375364477}{208211034}e^{2} - \frac{1773097362583}{208211034}e - \frac{87135410207}{208211034}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ | $\phantom{-}\frac{81858805}{104105517}e^{16} + \frac{247478139}{34701839}e^{15} + \frac{1578409721}{208211034}e^{14} - \frac{11099788390}{104105517}e^{13} - \frac{62424398437}{208211034}e^{12} + \frac{49069332340}{104105517}e^{11} + \frac{84368970786}{34701839}e^{10} + \frac{804288643}{104105517}e^{9} - \frac{898118075233}{104105517}e^{8} - \frac{1079453031101}{208211034}e^{7} + \frac{510408030790}{34701839}e^{6} + \frac{1393405467199}{104105517}e^{5} - \frac{1147716800603}{104105517}e^{4} - \frac{420648822945}{34701839}e^{3} + \frac{241416028343}{104105517}e^{2} + \frac{615261086281}{208211034}e + \frac{27116992469}{208211034}$ |
| 61 | $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ | $-\frac{60239}{157497}e^{16} - \frac{282341}{104998}e^{15} + \frac{296452}{157497}e^{14} + \frac{15323473}{314994}e^{13} + \frac{7286026}{157497}e^{12} - \frac{52779734}{157497}e^{11} - \frac{26862226}{52499}e^{10} + \frac{176456794}{157497}e^{9} + \frac{645786673}{314994}e^{8} - \frac{303810208}{157497}e^{7} - \frac{199287679}{52499}e^{6} + \frac{263550112}{157497}e^{5} + \frac{480528175}{157497}e^{4} - \frac{34461786}{52499}e^{3} - \frac{217363385}{314994}e^{2} + \frac{21996475}{314994}e - \frac{788186}{157497}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}\frac{168459735}{34701839}e^{16} + \frac{1456451387}{34701839}e^{15} + \frac{1100520346}{34701839}e^{14} - \frac{22609395269}{34701839}e^{13} - \frac{54872583182}{34701839}e^{12} + \frac{111940959759}{34701839}e^{11} + \frac{457850950080}{34701839}e^{10} - \frac{111497199756}{34701839}e^{9} - \frac{1647058845363}{34701839}e^{8} - \frac{662817699469}{34701839}e^{7} + \frac{2837651580152}{34701839}e^{6} + \frac{2038581393250}{34701839}e^{5} - \frac{2147460463131}{34701839}e^{4} - \frac{1927819426601}{34701839}e^{3} + \frac{455997978970}{34701839}e^{2} + \frac{477957265179}{34701839}e + \frac{22548210187}{34701839}$ |
| 64 | $[64, 2, -2]$ | $-\frac{780928397}{208211034}e^{16} - \frac{3400269140}{104105517}e^{15} - \frac{5452326937}{208211034}e^{14} + \frac{17500638969}{34701839}e^{13} + \frac{130314287183}{104105517}e^{12} - \frac{85362842717}{34701839}e^{11} - \frac{360756901326}{34701839}e^{10} + \frac{445819329913}{208211034}e^{9} + \frac{3884990396366}{104105517}e^{8} + \frac{1676705983946}{104105517}e^{7} - \frac{6683618836124}{104105517}e^{6} - \frac{4984155074270}{104105517}e^{5} + \frac{5053402227163}{104105517}e^{4} + \frac{9355982451661}{208211034}e^{3} - \frac{2147581272149}{208211034}e^{2} - \frac{1156549178098}{104105517}e - \frac{18088994631}{34701839}$ |
| 67 | $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ | $-\frac{14945053}{208211034}e^{16} - \frac{70648496}{104105517}e^{15} - \frac{57286571}{69403678}e^{14} + \frac{1068624247}{104105517}e^{13} + \frac{3165619618}{104105517}e^{12} - \frac{4865009617}{104105517}e^{11} - \frac{8643973261}{34701839}e^{10} + \frac{2100962009}{208211034}e^{9} + \frac{31491961446}{34701839}e^{8} + \frac{16078993102}{34701839}e^{7} - \frac{168032861195}{104105517}e^{6} - \frac{42452503160}{34701839}e^{5} + \frac{45082260938}{34701839}e^{4} + \frac{227485301173}{208211034}e^{3} - \frac{23116330809}{69403678}e^{2} - \frac{8555511354}{34701839}e - \frac{145811458}{104105517}$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ | $-\frac{1024969495}{208211034}e^{16} - \frac{9049978079}{208211034}e^{15} - \frac{4060684132}{104105517}e^{14} + \frac{45974966913}{69403678}e^{13} + \frac{359045396525}{208211034}e^{12} - \frac{107929722358}{34701839}e^{11} - \frac{492071276243}{34701839}e^{10} + \frac{347909465333}{208211034}e^{9} + \frac{10540769472185}{208211034}e^{8} + \frac{5323829701667}{208211034}e^{7} - \frac{9024097274026}{104105517}e^{6} - \frac{7392406182004}{104105517}e^{5} + \frac{6788899288802}{104105517}e^{4} + \frac{13658384836775}{208211034}e^{3} - \frac{1431542103218}{104105517}e^{2} - \frac{1678310063456}{104105517}e - \frac{52868977317}{69403678}$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ | $-\frac{64168444}{104105517}e^{16} - \frac{589102472}{104105517}e^{15} - \frac{1366585351}{208211034}e^{14} + \frac{2882336531}{34701839}e^{13} + \frac{50993440915}{208211034}e^{12} - \frac{12021536487}{34701839}e^{11} - \frac{68050404940}{34701839}e^{10} - \frac{20111016655}{104105517}e^{9} + \frac{717151022963}{104105517}e^{8} + \frac{983467960957}{208211034}e^{7} - \frac{1210405994948}{104105517}e^{6} - \frac{1209138977219}{104105517}e^{5} + \frac{899089516327}{104105517}e^{4} + \frac{1077936933089}{104105517}e^{3} - \frac{188983073752}{104105517}e^{2} - \frac{521704961117}{208211034}e - \frac{7837693061}{69403678}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}\frac{24800321}{104105517}e^{16} + \frac{242180515}{104105517}e^{15} + \frac{375845020}{104105517}e^{14} - \frac{1124815262}{34701839}e^{13} - \frac{11914256923}{104105517}e^{12} + \frac{3754408039}{34701839}e^{11} + \frac{31115245670}{34701839}e^{10} + \frac{35532386699}{104105517}e^{9} - \frac{325732708588}{104105517}e^{8} - \frac{304061459161}{104105517}e^{7} + \frac{548508234625}{104105517}e^{6} + \frac{687783912457}{104105517}e^{5} - \frac{407542897589}{104105517}e^{4} - \frac{601724431732}{104105517}e^{3} + \frac{86308838957}{104105517}e^{2} + \frac{143532549515}{104105517}e + \frac{2118234831}{34701839}$ |
| 81 | $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{951717863}{208211034}e^{16} + \frac{1390273280}{34701839}e^{15} + \frac{3537583696}{104105517}e^{14} - \frac{63971717362}{104105517}e^{13} - \frac{325082460991}{208211034}e^{12} + \frac{306160818415}{104105517}e^{11} + \frac{447614353666}{34701839}e^{10} - \frac{433421749633}{208211034}e^{9} - \frac{4804846268950}{104105517}e^{8} - \frac{4504880325689}{208211034}e^{7} + \frac{2746490792742}{34701839}e^{6} + \frac{6452033929417}{104105517}e^{5} - \frac{6203609613839}{104105517}e^{4} - \frac{4000890703331}{69403678}e^{3} + \frac{2610175273285}{208211034}e^{2} + \frac{2956878246775}{208211034}e + \frac{143506725335}{208211034}$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ | $-\frac{160048023}{69403678}e^{16} - \frac{4496417615}{208211034}e^{15} - \frac{5634894211}{208211034}e^{14} + \frac{65658276485}{208211034}e^{13} + \frac{33452105075}{34701839}e^{12} - \frac{134353141258}{104105517}e^{11} - \frac{266709191809}{34701839}e^{10} - \frac{67277082995}{69403678}e^{9} + \frac{5624232871357}{208211034}e^{8} + \frac{1962491318501}{104105517}e^{7} - \frac{4755799274263}{104105517}e^{6} - \frac{4765876704107}{104105517}e^{5} + \frac{3535914957604}{104105517}e^{4} + \frac{8465566340123}{208211034}e^{3} - \frac{734544579592}{104105517}e^{2} - \frac{2044233202199}{208211034}e - \frac{47604502825}{104105517}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $37$ | $[37,37,-w^{3} + 2w^{2} + 3w - 2]$ | $-1$ |