Base field 4.4.18097.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ |
| Dimension: | $18$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{18} - 8x^{17} - 4x^{16} + 188x^{15} - 345x^{14} - 1362x^{13} + 4655x^{12} + 1680x^{11} - 21475x^{10} + 16572x^{9} + 34568x^{8} - 57336x^{7} + 3372x^{6} + 44444x^{5} - 31243x^{4} + 5362x^{3} + 1348x^{2} - 456x + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w]$ | $\phantom{-}\frac{494568743648429}{21010248265029280}e^{17} - \frac{2186287045525303}{10505124132514640}e^{16} - \frac{305308582883}{262628103312866}e^{15} + \frac{25572094120900043}{5252562066257320}e^{14} - \frac{224964544016494317}{21010248265029280}e^{13} - \frac{182409074751134929}{5252562066257320}e^{12} + \frac{2864420494502560891}{21010248265029280}e^{11} + \frac{368287327995178707}{10505124132514640}e^{10} - \frac{13318560621562357979}{21010248265029280}e^{9} + \frac{5082197143899620731}{10505124132514640}e^{8} + \frac{1162903603519917809}{1050512413251464}e^{7} - \frac{2179813234278309479}{1313140516564330}e^{6} - \frac{1081393496127563097}{5252562066257320}e^{5} + \frac{7481441214757104561}{5252562066257320}e^{4} - \frac{13780597424293403431}{21010248265029280}e^{3} - \frac{149155658245757369}{5252562066257320}e^{2} + \frac{227787221151280947}{5252562066257320}e - \frac{2456603203680247}{1313140516564330}$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ | $\phantom{-}\frac{969241099341877}{21010248265029280}e^{17} - \frac{4094190264016939}{10505124132514640}e^{16} - \frac{12321837318825}{262628103312866}e^{15} + \frac{47070149180780499}{5252562066257320}e^{14} - \frac{410663355349220661}{21010248265029280}e^{13} - \frac{319795990355259467}{5252562066257320}e^{12} + \frac{5229706330561429283}{21010248265029280}e^{11} + \frac{270203719526002471}{10505124132514640}e^{10} - \frac{23650979404566976307}{21010248265029280}e^{9} + \frac{11265023735689794423}{10505124132514640}e^{8} + \frac{1866017649391376273}{1050512413251464}e^{7} - \frac{4437443758722149857}{1313140516564330}e^{6} + \frac{1351665118832227159}{5252562066257320}e^{5} + \frac{14168552456419441113}{5252562066257320}e^{4} - \frac{36163456452065462143}{21010248265029280}e^{3} + \frac{665440088179324793}{5252562066257320}e^{2} + \frac{600185849316999751}{5252562066257320}e - \frac{21338161806125771}{1313140516564330}$ |
| 7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ | $\phantom{-}\frac{158746952771385}{1050512413251464}e^{17} - \frac{655030453646935}{525256206625732}e^{16} - \frac{56565627147661}{131314051656433}e^{15} + \frac{7698897770584179}{262628103312866}e^{14} - \frac{59986540212126889}{1050512413251464}e^{13} - \frac{55742713217003995}{262628103312866}e^{12} + \frac{795361584264235583}{1050512413251464}e^{11} + \frac{134553562810069839}{525256206625732}e^{10} - \frac{3699208501909990055}{1050512413251464}e^{9} + \frac{1393526129980109543}{525256206625732}e^{8} + \frac{1557249812737102535}{262628103312866}e^{7} - \frac{1218614174889033036}{131314051656433}e^{6} - \frac{82927942163443989}{262628103312866}e^{5} + \frac{2010800098792160045}{262628103312866}e^{4} - \frac{4648597962823950419}{1050512413251464}e^{3} + \frac{76212450050203199}{262628103312866}e^{2} + \frac{73755848190106305}{262628103312866}e - \frac{4930820072918406}{131314051656433}$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $\phantom{-}\frac{2555075177055383}{10505124132514640}e^{17} - \frac{9737551532470481}{5252562066257320}e^{16} - \frac{223684959352283}{131314051656433}e^{15} + \frac{118683578559956141}{2626281033128660}e^{14} - \frac{693708246895457479}{10505124132514640}e^{13} - \frac{943667637191897353}{2626281033128660}e^{12} + \frac{10387177263410950497}{10505124132514640}e^{11} + \frac{4283680290519915709}{5252562066257320}e^{10} - \frac{51306125897556572913}{10505124132514640}e^{9} + \frac{10580990774680898917}{5252562066257320}e^{8} + \frac{4792987152540670519}{525256206625732}e^{7} - \frac{6604009688723815198}{656570258282165}e^{6} - \frac{7918653029711774399}{2626281033128660}e^{5} + \frac{23982612209565663607}{2626281033128660}e^{4} - \frac{42167544008572772917}{10505124132514640}e^{3} + \frac{130096614758909927}{2626281033128660}e^{2} + \frac{663724638836164609}{2626281033128660}e - \frac{21137400703440169}{656570258282165}$ |
| 17 | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ | $-1$ |
| 27 | $[27, 3, -w^{3} + 7w + 1]$ | $-\frac{488395678011819}{5252562066257320}e^{17} + \frac{418765584446677}{656570258282165}e^{16} + \frac{144574938645795}{131314051656433}e^{15} - \frac{21357263610983723}{1313140516564330}e^{14} + \frac{71589861151597787}{5252562066257320}e^{13} + \frac{375900271358969983}{2626281033128660}e^{12} - \frac{1434380299556390481}{5252562066257320}e^{11} - \frac{311779354045541768}{656570258282165}e^{10} + \frac{7839103330358923589}{5252562066257320}e^{9} + \frac{228484899901679487}{1313140516564330}e^{8} - \frac{837035680360570335}{262628103312866}e^{7} + \frac{1156658546465600253}{656570258282165}e^{6} + \frac{2674864431420825227}{1313140516564330}e^{5} - \frac{2729277372855451711}{1313140516564330}e^{4} + \frac{1693627362480851041}{5252562066257320}e^{3} + \frac{322782109913008513}{2626281033128660}e^{2} - \frac{16650206723717166}{656570258282165}e - \frac{22066097831936}{656570258282165}$ |
| 31 | $[31, 31, w + 3]$ | $\phantom{-}\frac{698989882338581}{10505124132514640}e^{17} - \frac{2991005364761797}{5252562066257320}e^{16} + \frac{2934228002274}{131314051656433}e^{15} + \frac{33645759118109907}{2626281033128660}e^{14} - \frac{317799376879015653}{10505124132514640}e^{13} - \frac{106901362927853403}{1313140516564330}e^{12} + \frac{3915870878574415259}{10505124132514640}e^{11} - \frac{185896251353326087}{5252562066257320}e^{10} - \frac{17077162063384635491}{10505124132514640}e^{9} + \frac{9843594996595108789}{5252562066257320}e^{8} + \frac{1202971907153789713}{525256206625732}e^{7} - \frac{3583490235709873246}{656570258282165}e^{6} + \frac{3227200944846679167}{2626281033128660}e^{5} + \frac{10706518658608302329}{2626281033128660}e^{4} - \frac{33916017563535768239}{10505124132514640}e^{3} + \frac{274895944594019811}{656570258282165}e^{2} + \frac{548271394519300433}{2626281033128660}e - \frac{18542630934877723}{656570258282165}$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $\phantom{-}\frac{276026763902731}{10505124132514640}e^{17} - \frac{1195731303469347}{5252562066257320}e^{16} + \frac{10196477821164}{131314051656433}e^{15} + \frac{12703391681729637}{2626281033128660}e^{14} - \frac{141322059543867723}{10505124132514640}e^{13} - \frac{32613142145650423}{1313140516564330}e^{12} + \frac{1636824157631278389}{10505124132514640}e^{11} - \frac{474574695949830177}{5252562066257320}e^{10} - \frac{6556703848592856301}{10505124132514640}e^{9} + \frac{5695368069354887579}{5252562066257320}e^{8} + \frac{318728315677064499}{525256206625732}e^{7} - \frac{1847433032323543206}{656570258282165}e^{6} + \frac{3500871891754949017}{2626281033128660}e^{5} + \frac{5146807753180955499}{2626281033128660}e^{4} - \frac{21073488547452194929}{10505124132514640}e^{3} + \frac{193179064021472991}{656570258282165}e^{2} + \frac{397675011612312903}{2626281033128660}e - \frac{11769814717702253}{656570258282165}$ |
| 37 | $[37, 37, w^{2} - 3]$ | $-\frac{1680832519607677}{10505124132514640}e^{17} + \frac{6012713832156749}{5252562066257320}e^{16} + \frac{213192736778045}{131314051656433}e^{15} - \frac{75587078842193579}{2626281033128660}e^{14} + \frac{321220918377471581}{10505124132514640}e^{13} + \frac{322510741506852071}{1313140516564330}e^{12} - \frac{5636786300538927123}{10505124132514640}e^{11} - \frac{3874823134900598801}{5252562066257320}e^{10} + \frac{29713886123055016267}{10505124132514640}e^{9} - \frac{1143114410302245253}{5252562066257320}e^{8} - \frac{3058544550547977521}{525256206625732}e^{7} + \frac{2812001684181354122}{656570258282165}e^{6} + \frac{8643483921566932781}{2626281033128660}e^{5} - \frac{12147742095805073333}{2626281033128660}e^{4} + \frac{11172245116517951063}{10505124132514640}e^{3} + \frac{213995841849983828}{656570258282165}e^{2} - \frac{243859791319939961}{2626281033128660}e + \frac{1035971526023781}{656570258282165}$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ | $\phantom{-}\frac{2049321665473143}{10505124132514640}e^{17} - \frac{7218659922286781}{5252562066257320}e^{16} - \frac{281300811162917}{131314051656433}e^{15} + \frac{91565771814015521}{2626281033128660}e^{14} - \frac{346563330160757159}{10505124132514640}e^{13} - \frac{797093484686900623}{2626281033128660}e^{12} + \frac{6448837883120622417}{10505124132514640}e^{11} + \frac{5119246648408904369}{5252562066257320}e^{10} - \frac{34559723048291710593}{10505124132514640}e^{9} - \frac{846812422063397783}{5252562066257320}e^{8} + \frac{3618394781797473955}{525256206625732}e^{7} - \frac{2754821468481784613}{656570258282165}e^{6} - \frac{10878773833621334119}{2626281033128660}e^{5} + \frac{12259203321295964187}{2626281033128660}e^{4} - \frac{9988670177668323957}{10505124132514640}e^{3} - \frac{389682216256828823}{2626281033128660}e^{2} + \frac{84864961988894789}{2626281033128660}e - \frac{2419499612594629}{656570258282165}$ |
| 47 | $[47, 47, w^{3} - 5w - 3]$ | $-\frac{1141760867358281}{10505124132514640}e^{17} + \frac{3309620428064487}{5252562066257320}e^{16} + \frac{253756949091086}{131314051656433}e^{15} - \frac{44824243435919527}{2626281033128660}e^{14} - \frac{7616235301177207}{10505124132514640}e^{13} + \frac{442446507267268871}{2626281033128660}e^{12} - \frac{1774833234417428319}{10505124132514640}e^{11} - \frac{3865000482486445363}{5252562066257320}e^{10} + \frac{12709579041119579071}{10505124132514640}e^{9} + \frac{7022946772578657341}{5252562066257320}e^{8} - \frac{1736843313529817877}{525256206625732}e^{7} - \frac{282152220543845739}{656570258282165}e^{6} + \frac{9654087557701748373}{2626281033128660}e^{5} - \frac{2513807738527208429}{2626281033128660}e^{4} - \frac{14394231298688111461}{10505124132514640}e^{3} + \frac{1465899761136781731}{2626281033128660}e^{2} + \frac{158226317115927017}{2626281033128660}e - \frac{12277614070976647}{656570258282165}$ |
| 53 | $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ | $\phantom{-}\frac{1514229209912701}{2626281033128660}e^{17} - \frac{11596357103158489}{2626281033128660}e^{16} - \frac{488099744001386}{131314051656433}e^{15} + \frac{69935439944630437}{656570258282165}e^{14} - \frac{430614701088817733}{2626281033128660}e^{13} - \frac{2168309625673040649}{2626281033128660}e^{12} + \frac{6290168005836219389}{2626281033128660}e^{11} + \frac{4321532795742179761}{2626281033128660}e^{10} - \frac{30482157860709818051}{2626281033128660}e^{9} + \frac{15999725102198937443}{2626281033128660}e^{8} + \frac{2726709886960862058}{131314051656433}e^{7} - \frac{17302303011912294764}{656570258282165}e^{6} - \frac{2826260257601330883}{656570258282165}e^{5} + \frac{15044678913309449339}{656570258282165}e^{4} - \frac{31580798571340152759}{2626281033128660}e^{3} + \frac{1747659884002514861}{2626281033128660}e^{2} + \frac{1036673721969036681}{1313140516564330}e - \frac{65171199150039232}{656570258282165}$ |
| 61 | $[61, 61, w^{3} - w^{2} - 5w + 3]$ | $-\frac{3602727944630249}{10505124132514640}e^{17} + \frac{14308784972040823}{5252562066257320}e^{16} + \frac{193570671274821}{131314051656433}e^{15} - \frac{168604928654964763}{2626281033128660}e^{14} + \frac{1218766303423040777}{10505124132514640}e^{13} + \frac{1229790022127023059}{2626281033128660}e^{12} - \frac{16615670256550576751}{10505124132514640}e^{11} - \frac{3196126602767767267}{5252562066257320}e^{10} + \frac{77400138204899144799}{10505124132514640}e^{9} - \frac{29162725570382316971}{5252562066257320}e^{8} - \frac{6387471745349575333}{525256206625732}e^{7} + \frac{12919283707242311544}{656570258282165}e^{6} - \frac{805205966886496443}{2626281033128660}e^{5} - \frac{42159971833468256841}{2626281033128660}e^{4} + \frac{107439593545554309051}{10505124132514640}e^{3} - \frac{2412352554136842541}{2626281033128660}e^{2} - \frac{1829344242912473827}{2626281033128660}e + \frac{61757171194043827}{656570258282165}$ |
| 83 | $[83, 83, w^{3} + w^{2} - 6w - 7]$ | $\phantom{-}\frac{1431382487097451}{5252562066257320}e^{17} - \frac{2962611932544461}{1313140516564330}e^{16} - \frac{95266901546782}{131314051656433}e^{15} + \frac{69452093472380877}{1313140516564330}e^{14} - \frac{546671871419547283}{5252562066257320}e^{13} - \frac{998522420972909017}{2626281033128660}e^{12} + \frac{7202433810654028929}{5252562066257320}e^{11} + \frac{562492083242499859}{1313140516564330}e^{10} - \frac{33258617029040142701}{5252562066257320}e^{9} + \frac{3239352031150663561}{656570258282165}e^{8} + \frac{2744749348887766491}{262628103312866}e^{7} - \frac{11128045484229535012}{656570258282165}e^{6} + \frac{120781471078370837}{1313140516564330}e^{5} + \frac{17988803088086665679}{1313140516564330}e^{4} - \frac{44763969066277942049}{5252562066257320}e^{3} + \frac{2139101503399046773}{2626281033128660}e^{2} + \frac{349567630300932179}{656570258282165}e - \frac{52259813585564596}{656570258282165}$ |
| 83 | $[83, 83, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{1060413023054307}{2101024826502928}e^{17} - \frac{4061568526831943}{1050512413251464}e^{16} - \frac{421829506762088}{131314051656433}e^{15} + \frac{48885070354324649}{525256206625732}e^{14} - \frac{303440784758519571}{2101024826502928}e^{13} - \frac{94221069212078473}{131314051656433}e^{12} + \frac{4415451687640239709}{2101024826502928}e^{11} + \frac{1456983549276005867}{1050512413251464}e^{10} - \frac{21322626886219800229}{2101024826502928}e^{9} + \frac{5857347614466226071}{1050512413251464}e^{8} + \frac{9456918441327228379}{525256206625732}e^{7} - \frac{3092239110421260563}{131314051656433}e^{6} - \frac{1735323893433707855}{525256206625732}e^{5} + \frac{10691197363237632739}{525256206625732}e^{4} - \frac{22865293728527856729}{2101024826502928}e^{3} + \frac{167070131497300161}{262628103312866}e^{2} + \frac{364612109460480435}{525256206625732}e - \frac{11967649908655877}{131314051656433}$ |
| 83 | $[83, 83, 2w - 1]$ | $-\frac{38532169455557}{2101024826502928}e^{17} - \frac{84437751960795}{1050512413251464}e^{16} + \frac{208309480786426}{131314051656433}e^{15} - \frac{293040921180131}{525256206625732}e^{14} - \frac{68042805486564411}{2101024826502928}e^{13} + \frac{13868967564410555}{262628103312866}e^{12} + \frac{541460692162348885}{2101024826502928}e^{11} - \frac{676043307987354457}{1050512413251464}e^{10} - \frac{1612896926395899325}{2101024826502928}e^{9} + \frac{3256536272791737955}{1050512413251464}e^{8} - \frac{34970668522698109}{525256206625732}e^{7} - \frac{822717618762271598}{131314051656433}e^{6} + \frac{2002995183306886421}{525256206625732}e^{5} + \frac{2041577219171106163}{525256206625732}e^{4} - \frac{8696862527391369281}{2101024826502928}e^{3} + \frac{80795184961141576}{131314051656433}e^{2} + \frac{122457301632510079}{525256206625732}e - \frac{4437125485094265}{131314051656433}$ |
| 83 | $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ | $-\frac{472258497365083}{5252562066257320}e^{17} + \frac{308815721476569}{656570258282165}e^{16} + \frac{249399278986832}{131314051656433}e^{15} - \frac{17536125778965741}{1313140516564330}e^{14} - \frac{43289160492197021}{5252562066257320}e^{13} + \frac{373955816784105391}{2626281033128660}e^{12} - \frac{383253686837415337}{5252562066257320}e^{11} - \frac{468427728463182991}{656570258282165}e^{10} + \frac{4117823953236989053}{5252562066257320}e^{9} + \frac{2255555006626195449}{1313140516564330}e^{8} - \frac{705949591877058401}{262628103312866}e^{7} - \frac{1096267260120194114}{656570258282165}e^{6} + \frac{5194477342032218699}{1313140516564330}e^{5} - \frac{32989296375844137}{1313140516564330}e^{4} - \frac{11579520846940022783}{5252562066257320}e^{3} + \frac{1856709699417507361}{2626281033128660}e^{2} + \frac{87926218696565783}{656570258282165}e - \frac{27217811679311932}{656570258282165}$ |
| 89 | $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ | $\phantom{-}\frac{5478854292924193}{10505124132514640}e^{17} - \frac{21365015686364961}{5252562066257320}e^{16} - \frac{390948250035391}{131314051656433}e^{15} + \frac{256658547581486871}{2626281033128660}e^{14} - \frac{1664033890571381969}{10505124132514640}e^{13} - \frac{984648294539612379}{1313140516564330}e^{12} + \frac{23744319546851314607}{10505124132514640}e^{11} + \frac{7406344098638396629}{5252562066257320}e^{10} - \frac{114079127092882576823}{10505124132514640}e^{9} + \frac{31916886979825354977}{5252562066257320}e^{8} + \frac{10096381146227873869}{525256206625732}e^{7} - \frac{16516156000513098053}{656570258282165}e^{6} - \frac{9197661358411103429}{2626281033128660}e^{5} + \frac{56719837327166733797}{2626281033128660}e^{4} - \frac{122581733910022036867}{10505124132514640}e^{3} + \frac{485310977507147338}{656570258282165}e^{2} + \frac{2073825630963610569}{2626281033128660}e - \frac{69590141640639009}{656570258282165}$ |
| 89 | $[89, 89, w^{3} - 5w + 5]$ | $\phantom{-}\frac{441486310501163}{2101024826502928}e^{17} - \frac{1807897429270047}{1050512413251464}e^{16} - \frac{87367666359554}{131314051656433}e^{15} + \frac{21299289594709117}{525256206625732}e^{14} - \frac{163434187776791307}{2101024826502928}e^{13} - \frac{38794777320018750}{131314051656433}e^{12} + \frac{2184909216486924341}{2101024826502928}e^{11} + \frac{396511168013400875}{1050512413251464}e^{10} - \frac{10224143105162675229}{2101024826502928}e^{9} + \frac{3744890494663575815}{1050512413251464}e^{8} + \frac{4363107932275243963}{525256206625732}e^{7} - \frac{1662857384108598875}{131314051656433}e^{6} - \frac{399505109685022511}{525256206625732}e^{5} + \frac{5560613830740446711}{525256206625732}e^{4} - \frac{12357941907484156993}{2101024826502928}e^{3} + \frac{69464807278171277}{262628103312866}e^{2} + \frac{224166477522664647}{525256206625732}e - \frac{6232710461136011}{131314051656433}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ | $1$ |