Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} - w + 3]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + 7x^{19} - 6x^{18} - 138x^{17} - 133x^{16} + 1070x^{15} + 1820x^{14} - 4096x^{13} - 9348x^{12} + 7866x^{11} + 24258x^{10} - 6530x^{9} - 33216x^{8} + 1128x^{7} + 23505x^{6} - 284x^{5} - 8657x^{4} + 821x^{3} + 1359x^{2} - 278x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $-\frac{617511}{275090}e^{19} - \frac{941187}{55018}e^{18} + \frac{483048}{137545}e^{17} + \frac{43442373}{137545}e^{16} + \frac{133947461}{275090}e^{15} - \frac{299660091}{137545}e^{14} - \frac{749094828}{137545}e^{13} + \frac{888124399}{137545}e^{12} + \frac{3507145696}{137545}e^{11} - \frac{123855366}{27509}e^{10} - \frac{8281518014}{137545}e^{9} - \frac{2299116692}{137545}e^{8} + \frac{9873916227}{137545}e^{7} + \frac{4796733197}{137545}e^{6} - \frac{11112071623}{275090}e^{5} - \frac{551288333}{27509}e^{4} + \frac{3265502907}{275090}e^{3} + \frac{213148503}{55018}e^{2} - \frac{441014959}{275090}e - \frac{9045642}{137545}$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $\phantom{-}\frac{56392}{137545}e^{19} + \frac{94526}{27509}e^{18} + \frac{214898}{137545}e^{17} - \frac{8103617}{137545}e^{16} - \frac{17773177}{137545}e^{15} + \frac{47875814}{137545}e^{14} + \frac{174468267}{137545}e^{13} - \frac{82438981}{137545}e^{12} - \frac{749261094}{137545}e^{11} - \frac{49134390}{27509}e^{10} + \frac{1581281166}{137545}e^{9} + \frac{1182850613}{137545}e^{8} - \frac{1527297113}{137545}e^{7} - \frac{1587107693}{137545}e^{6} + \frac{508197056}{137545}e^{5} + \frac{137717526}{27509}e^{4} - \frac{83510194}{137545}e^{3} - \frac{19599116}{27509}e^{2} + \frac{12963198}{137545}e - \frac{32177}{137545}$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $-\frac{776809}{275090}e^{19} - \frac{1176021}{55018}e^{18} + \frac{734527}{137545}e^{17} + \frac{54495127}{137545}e^{16} + \frac{163682519}{275090}e^{15} - \frac{378690879}{137545}e^{14} - \frac{924805152}{137545}e^{13} + \frac{1143379941}{137545}e^{12} + \frac{4352547339}{137545}e^{11} - \frac{181295658}{27509}e^{10} - \frac{10334371221}{137545}e^{9} - \frac{2603233068}{137545}e^{8} + \frac{12420224958}{137545}e^{7} + \frac{5735324648}{137545}e^{6} - \frac{14144327927}{275090}e^{5} - \frac{671156864}{27509}e^{4} + \frac{4156565223}{275090}e^{3} + \frac{261196855}{55018}e^{2} - \frac{552892831}{275090}e - \frac{11226108}{137545}$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $-\frac{1141177}{275090}e^{19} - \frac{1692399}{55018}e^{18} + \frac{1703466}{137545}e^{17} + \frac{79613191}{137545}e^{16} + \frac{216689417}{275090}e^{15} - \frac{568871987}{137545}e^{14} - \frac{1271400091}{137545}e^{13} + \frac{1835805138}{137545}e^{12} + \frac{6091855912}{137545}e^{11} - \frac{412918417}{27509}e^{10} - \frac{14719526038}{137545}e^{9} - \frac{2170368094}{137545}e^{8} + \frac{18129955709}{137545}e^{7} + \frac{6681816089}{137545}e^{6} - \frac{21444853761}{275090}e^{5} - \frac{845865499}{27509}e^{4} + \frac{6401082919}{275090}e^{3} + \frac{344033515}{55018}e^{2} - \frac{832165963}{275090}e - \frac{15880599}{137545}$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $-\frac{635442}{137545}e^{19} - \frac{959691}{27509}e^{18} + \frac{1156147}{137545}e^{17} + \frac{88222902}{137545}e^{16} + \frac{133108762}{137545}e^{15} - \frac{604447079}{137545}e^{14} - \frac{1485965552}{137545}e^{13} + \frac{1767212796}{137545}e^{12} + \frac{6875119674}{137545}e^{11} - \frac{228862233}{27509}e^{10} - \frac{15863270741}{137545}e^{9} - \frac{4726673568}{137545}e^{8} + \frac{18069582918}{137545}e^{7} + \frac{9382019243}{137545}e^{6} - \frac{9251008566}{137545}e^{5} - \frac{999535128}{27509}e^{4} + \frac{2471898579}{137545}e^{3} + \frac{177530662}{27509}e^{2} - \frac{317818748}{137545}e - \frac{12834408}{137545}$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $\phantom{-}\frac{110411}{55018}e^{19} + \frac{832935}{55018}e^{18} - \frac{120172}{27509}e^{17} - \frac{7788698}{27509}e^{16} - \frac{22916663}{55018}e^{15} + \frac{54940042}{27509}e^{14} + \frac{131757032}{27509}e^{13} - \frac{171266921}{27509}e^{12} - \frac{630885520}{27509}e^{11} + \frac{159489754}{27509}e^{10} + \frac{1536107849}{27509}e^{9} + \frac{325206883}{27509}e^{8} - \frac{1925608117}{27509}e^{7} - \frac{810962577}{27509}e^{6} + \frac{2354202013}{55018}e^{5} + \frac{517999328}{27509}e^{4} - \frac{727058041}{55018}e^{3} - \frac{215315389}{55018}e^{2} + \frac{98391185}{55018}e + \frac{1888955}{27509}$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $-\frac{280576}{137545}e^{19} - \frac{414375}{27509}e^{18} + \frac{933821}{137545}e^{17} + \frac{39513796}{137545}e^{16} + \frac{52633391}{137545}e^{15} - \frac{288486542}{137545}e^{14} - \frac{635990146}{137545}e^{13} + \frac{970164563}{137545}e^{12} + \frac{3145569082}{137545}e^{11} - \frac{249624168}{27509}e^{10} - \frac{7968652888}{137545}e^{9} - \frac{737145409}{137545}e^{8} + \frac{10603574094}{137545}e^{7} + \frac{3288739459}{137545}e^{6} - \frac{7090145603}{137545}e^{5} - \frac{488712403}{27509}e^{4} + \frac{2326825142}{137545}e^{3} + \frac{111507237}{27509}e^{2} - \frac{314335094}{137545}e - \frac{12637424}{137545}$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}\frac{367377}{27509}e^{19} + \frac{2741326}{27509}e^{18} - \frac{934379}{27509}e^{17} - \frac{51107005}{27509}e^{16} - \frac{72502800}{27509}e^{15} + \frac{359160959}{27509}e^{14} + \frac{834337275}{27509}e^{13} - \frac{1115992189}{27509}e^{12} - \frac{3945911381}{27509}e^{11} + \frac{1054425046}{27509}e^{10} + \frac{9379300505}{27509}e^{9} + \frac{1956568178}{27509}e^{8} - \frac{11253846595}{27509}e^{7} - \frac{4800015598}{27509}e^{6} + \frac{6371140906}{27509}e^{5} + \frac{2836889992}{27509}e^{4} - \frac{1852683226}{27509}e^{3} - \frac{551669361}{27509}e^{2} + \frac{242306712}{27509}e + \frac{9397143}{27509}$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $\phantom{-}\frac{2815247}{275090}e^{19} + \frac{4237991}{55018}e^{18} - \frac{2945031}{137545}e^{17} - \frac{196394611}{137545}e^{16} - \frac{580373437}{275090}e^{15} + \frac{1365178907}{137545}e^{14} + \frac{3291406821}{137545}e^{13} - \frac{4127694873}{137545}e^{12} - \frac{15472504532}{137545}e^{11} + \frac{663769781}{27509}e^{10} + \frac{36586495718}{137545}e^{9} + \frac{9182728589}{137545}e^{8} - \frac{43595707659}{137545}e^{7} - \frac{20269508024}{137545}e^{6} + \frac{48819563371}{275090}e^{5} + \frac{2343729380}{27509}e^{4} - \frac{14128364649}{275090}e^{3} - \frac{899103107}{55018}e^{2} + \frac{1869298003}{275090}e + \frac{36026709}{137545}$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-\frac{2423502}{137545}e^{19} - \frac{3622460}{27509}e^{18} + \frac{5845997}{137545}e^{17} + \frac{336496642}{137545}e^{16} + \frac{482883752}{137545}e^{15} - \frac{2350134599}{137545}e^{14} - \frac{5519090862}{137545}e^{13} + \frac{7198931416}{137545}e^{12} + \frac{25950075629}{137545}e^{11} - \frac{1263307566}{27509}e^{10} - \frac{61164342991}{137545}e^{9} - \frac{14108398548}{137545}e^{8} + \frac{72303902108}{137545}e^{7} + \frac{32542664643}{137545}e^{6} - \frac{39794439541}{137545}e^{5} - \frac{3736148291}{27509}e^{4} + \frac{11282699659}{137545}e^{3} + \frac{708635522}{27509}e^{2} - \frac{1462721888}{137545}e - \frac{58641783}{137545}$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $-\frac{510679}{275090}e^{19} - \frac{697681}{55018}e^{18} + \frac{1676172}{137545}e^{17} + \frac{33982522}{137545}e^{16} + \frac{59240209}{275090}e^{15} - \frac{258559309}{137545}e^{14} - \frac{411906212}{137545}e^{13} + \frac{956108231}{137545}e^{12} + \frac{2049662424}{137545}e^{11} - \frac{338862084}{27509}e^{10} - \frac{4974485581}{137545}e^{9} + \frac{1022902122}{137545}e^{8} + \frac{5982991863}{137545}e^{7} + \frac{489617048}{137545}e^{6} - \frac{6536083087}{275090}e^{5} - \frac{100267169}{27509}e^{4} + \frac{1607539993}{275090}e^{3} + \frac{38037343}{55018}e^{2} - \frac{143705541}{275090}e - \frac{2839863}{137545}$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $\phantom{-}\frac{2147803}{137545}e^{19} + \frac{3215258}{27509}e^{18} - \frac{5103123}{137545}e^{17} - \frac{298887463}{137545}e^{16} - \frac{430206153}{137545}e^{15} + \frac{2089982771}{137545}e^{14} + \frac{4917565093}{137545}e^{13} - \frac{6418037549}{137545}e^{12} - \frac{23158173546}{137545}e^{11} + \frac{1139197197}{27509}e^{10} + \frac{54751631519}{137545}e^{9} + \frac{12424585122}{137545}e^{8} - \frac{65107597437}{137545}e^{7} - \frac{28974434507}{137545}e^{6} + \frac{36256031774}{137545}e^{5} + \frac{3363541100}{27509}e^{4} - \frac{10395235691}{137545}e^{3} - \frac{645200382}{27509}e^{2} + \frac{1355288632}{137545}e + \frac{54370467}{137545}$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-\frac{704567}{137545}e^{19} - \frac{1022202}{27509}e^{18} + \frac{2838947}{137545}e^{17} + \frac{97463987}{137545}e^{16} + \frac{119780567}{137545}e^{15} - \frac{712948964}{137545}e^{14} - \frac{1467320032}{137545}e^{13} + \frac{2420933341}{137545}e^{12} + \frac{7168891524}{137545}e^{11} - \frac{659320052}{27509}e^{10} - \frac{17651600061}{137545}e^{9} - \frac{982959768}{137545}e^{8} + \frac{22314470973}{137545}e^{7} + \frac{6479422858}{137545}e^{6} - \frac{13718772706}{137545}e^{5} - \frac{908660643}{27509}e^{4} + \frac{4172971924}{137545}e^{3} + \frac{194122570}{27509}e^{2} - \frac{533626558}{137545}e - \frac{19532673}{137545}$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $-\frac{258608}{137545}e^{19} - \frac{422942}{27509}e^{18} - \frac{637472}{137545}e^{17} + \frac{36955298}{137545}e^{16} + \frac{75643868}{137545}e^{15} - \frac{227462676}{137545}e^{14} - \frac{767122338}{137545}e^{13} + \frac{465920344}{137545}e^{12} + \frac{3395259606}{137545}e^{11} + \frac{152636614}{27509}e^{10} - \frac{7520841849}{137545}e^{9} - \frac{4777641737}{137545}e^{8} + \frac{8080869937}{137545}e^{7} + \frac{6961794982}{137545}e^{6} - \frac{3735452444}{137545}e^{5} - \frac{685691119}{27509}e^{4} + \frac{1008667096}{137545}e^{3} + \frac{117751614}{27509}e^{2} - \frac{161862117}{137545}e - \frac{4989957}{137545}$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $\phantom{-}\frac{1046162}{137545}e^{19} + \frac{1592272}{27509}e^{18} - \frac{1543752}{137545}e^{17} - \frac{146073352}{137545}e^{16} - \frac{226985537}{137545}e^{15} + \frac{996295829}{137545}e^{14} + \frac{2516942892}{137545}e^{13} - \frac{2873414801}{137545}e^{12} - \frac{11657220009}{137545}e^{11} + \frac{324636455}{27509}e^{10} + \frac{27050480011}{137545}e^{9} + \frac{8567256673}{137545}e^{8} - \frac{31233489388}{137545}e^{7} - \frac{16616022233}{137545}e^{6} + \frac{16510200671}{137545}e^{5} + \frac{1808230532}{27509}e^{4} - \frac{4601358984}{137545}e^{3} - \frac{330548040}{27509}e^{2} + \frac{615776963}{137545}e + \frac{22672078}{137545}$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}\frac{2187159}{275090}e^{19} + \frac{3277333}{55018}e^{18} - \frac{2715857}{137545}e^{17} - \frac{153328137}{137545}e^{16} - \frac{437361389}{275090}e^{15} + \frac{1084380839}{137545}e^{14} + \frac{2525085887}{137545}e^{13} - \frac{3414134696}{137545}e^{12} - \frac{12034729574}{137545}e^{11} + \frac{682612357}{27509}e^{10} + \frac{28992859206}{137545}e^{9} + \frac{5497419888}{137545}e^{8} - \frac{35636475773}{137545}e^{7} - \frac{14400297998}{137545}e^{6} + \frac{42121410157}{275090}e^{5} + \frac{1785306036}{27509}e^{4} - \frac{12653785283}{275090}e^{3} - \frac{722156045}{55018}e^{2} + \frac{1668328211}{275090}e + \frac{33671348}{137545}$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $-\frac{330869}{137545}e^{19} - \frac{483088}{27509}e^{18} + \frac{1168054}{137545}e^{17} + \frac{45605814}{137545}e^{16} + \frac{59335599}{137545}e^{15} - \frac{327632248}{137545}e^{14} - \frac{711192824}{137545}e^{13} + \frac{1068189247}{137545}e^{12} + \frac{3441252098}{137545}e^{11} - \frac{248735102}{27509}e^{10} - \frac{8401241677}{137545}e^{9} - \frac{1155148406}{137545}e^{8} + \frac{10516663431}{137545}e^{7} + \frac{3829844591}{137545}e^{6} - \frac{6402545477}{137545}e^{5} - \frac{504738870}{27509}e^{4} + \frac{1973488868}{137545}e^{3} + \frac{106353589}{27509}e^{2} - \frac{264425431}{137545}e - \frac{10343081}{137545}$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1253762}{137545}e^{19} + \frac{1885259}{27509}e^{18} - \frac{2758557}{137545}e^{17} - \frac{175126922}{137545}e^{16} - \frac{255928502}{137545}e^{15} + \frac{1222796574}{137545}e^{14} + \frac{2913527092}{137545}e^{13} - \frac{3740219466}{137545}e^{12} - \frac{13722097719}{137545}e^{11} + \frac{647225877}{27509}e^{10} + \frac{32511750316}{137545}e^{9} + \frac{7547093038}{137545}e^{8} - \frac{38852124513}{137545}e^{7} - \frac{17358049943}{137545}e^{6} + \frac{21851111436}{137545}e^{5} + \frac{2025409289}{27509}e^{4} - \frac{6323543964}{137545}e^{3} - \frac{391897644}{27509}e^{2} + \frac{829301333}{137545}e + \frac{34470163}{137545}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} - w + 3]$ | $-1$ |