Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11, 11, -3w - 17]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - 2x^{16} - 37x^{15} + 72x^{14} + 555x^{13} - 1033x^{12} - 4393x^{11} + 7592x^{10} + 20100x^{9} - 30534x^{8} - 55106x^{7} + 65879x^{6} + 91530x^{5} - 67293x^{4} - 89223x^{3} + 19019x^{2} + 39557x + 9277\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 6]$ | $-\frac{23606510938234962}{1658850077765614801}e^{16} + \frac{40465983917166655}{1658850077765614801}e^{15} + \frac{846302189400600501}{1658850077765614801}e^{14} - \frac{1412419779462654901}{1658850077765614801}e^{13} - \frac{12104154161951666293}{1658850077765614801}e^{12} + \frac{19389133604107522332}{1658850077765614801}e^{11} + \frac{88917682638702998102}{1658850077765614801}e^{10} - \frac{133629915892805990661}{1658850077765614801}e^{9} - \frac{360225309039509630383}{1658850077765614801}e^{8} + \frac{488166806647104853027}{1658850077765614801}e^{7} + \frac{804363311454769987689}{1658850077765614801}e^{6} - \frac{905222282690815147951}{1658850077765614801}e^{5} - \frac{946154494482977905097}{1658850077765614801}e^{4} + \frac{719048184521024101959}{1658850077765614801}e^{3} + \frac{542438602449870278667}{1658850077765614801}e^{2} - \frac{159347494806669405497}{1658850077765614801}e - \frac{90483618178027172443}{1658850077765614801}$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{6323029181899135}{1658850077765614801}e^{16} - \frac{35544485410841169}{3317700155531229602}e^{15} + \frac{523830985316090093}{3317700155531229602}e^{14} + \frac{1324534798702729315}{3317700155531229602}e^{13} - \frac{4449284678534327645}{1658850077765614801}e^{12} - \frac{9989184314611445649}{1658850077765614801}e^{11} + \frac{79761210981337726951}{3317700155531229602}e^{10} + \frac{78801371913702450351}{1658850077765614801}e^{9} - \frac{402645498775262600651}{3317700155531229602}e^{8} - \frac{700064205220262214519}{3317700155531229602}e^{7} + \frac{560624892661438735520}{1658850077765614801}e^{6} + \frac{1748126434520383918375}{3317700155531229602}e^{5} - \frac{756107817200846405662}{1658850077765614801}e^{4} - \frac{2287631280130399557825}{3317700155531229602}e^{3} + \frac{278666168626378930570}{1658850077765614801}e^{2} + \frac{626305352681735644402}{1658850077765614801}e + \frac{306384699903912862509}{3317700155531229602}$ |
| 11 | $[11, 11, -3w - 17]$ | $-1$ |
| 11 | $[11, 11, 3w - 20]$ | $-\frac{36048716835303643}{3317700155531229602}e^{16} + \frac{33066895787630717}{3317700155531229602}e^{15} + \frac{1342787698222913941}{3317700155531229602}e^{14} - \frac{532051533312777306}{1658850077765614801}e^{13} - \frac{10120808221887402599}{1658850077765614801}e^{12} + \frac{12816779027780128007}{3317700155531229602}e^{11} + \frac{79872532777130295678}{1658850077765614801}e^{10} - \frac{69724697629576236419}{3317700155531229602}e^{9} - \frac{711694252280191732159}{3317700155531229602}e^{8} + \frac{72473018182962818011}{1658850077765614801}e^{7} + \frac{1784647066736234562713}{3317700155531229602}e^{6} + \frac{54789048597592556765}{1658850077765614801}e^{5} - \frac{2314716907335978235315}{3317700155531229602}e^{4} - \frac{409330303297509759117}{1658850077765614801}e^{3} + \frac{571255889058330360918}{1658850077765614801}e^{2} + \frac{785740994466104746185}{3317700155531229602}e + \frac{64680450528852161251}{1658850077765614801}$ |
| 13 | $[13, 13, 2w - 13]$ | $\phantom{-}\frac{17894812222481269}{1658850077765614801}e^{16} + \frac{489050569348960}{1658850077765614801}e^{15} - \frac{682563400096847599}{1658850077765614801}e^{14} - \frac{75109232861934715}{1658850077765614801}e^{13} + \frac{10581001522170422200}{1658850077765614801}e^{12} + \frac{2241937527571578365}{1658850077765614801}e^{11} - \frac{86102801255568114004}{1658850077765614801}e^{10} - \frac{28657260751248958038}{1658850077765614801}e^{9} + \frac{395016062556020164632}{1658850077765614801}e^{8} + \frac{186659696047584266075}{1658850077765614801}e^{7} - \frac{1010211555941986676947}{1658850077765614801}e^{6} - \frac{644386671638460398938}{1658850077765614801}e^{5} + \frac{1293767375500754065941}{1658850077765614801}e^{4} + \frac{1116538395963200309784}{1658850077765614801}e^{3} - \frac{536104864338705132161}{1658850077765614801}e^{2} - \frac{757593849265746722019}{1658850077765614801}e - \frac{182100624988508032580}{1658850077765614801}$ |
| 13 | $[13, 13, 2w + 11]$ | $-\frac{42454752147054977}{1658850077765614801}e^{16} - \frac{21297547511024420}{1658850077765614801}e^{15} + \frac{1643605707437648438}{1658850077765614801}e^{14} + \frac{901661799302231237}{1658850077765614801}e^{13} - \frac{25941888873009399362}{1658850077765614801}e^{12} - \frac{15722319197005316293}{1658850077765614801}e^{11} + \frac{215632992728089844978}{1658850077765614801}e^{10} + \frac{145140970305868036701}{1658850077765614801}e^{9} - \frac{1013627941510136575683}{1658850077765614801}e^{8} - \frac{758989545472065300274}{1658850077765614801}e^{7} + \frac{2663206248760782000704}{1658850077765614801}e^{6} + \frac{2234907044207736707504}{1658850077765614801}e^{5} - \frac{3506549408069348501769}{1658850077765614801}e^{4} - \frac{3432271571976645415823}{1658850077765614801}e^{3} + \frac{1487561554526514108360}{1658850077765614801}e^{2} + \frac{2142714107505645114275}{1658850077765614801}e + \frac{490841283832641982190}{1658850077765614801}$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{20969327967687120}{1658850077765614801}e^{16} - \frac{34505681659973942}{1658850077765614801}e^{15} - \frac{750686906168912241}{1658850077765614801}e^{14} + \frac{1226192939393259930}{1658850077765614801}e^{13} + \frac{10678728050282162195}{1658850077765614801}e^{12} - \frac{17241987149485204668}{1658850077765614801}e^{11} - \frac{77384392507963766533}{1658850077765614801}e^{10} + \frac{122795380764910839807}{1658850077765614801}e^{9} + \frac{304362344199050645500}{1658850077765614801}e^{8} - \frac{470049532383424258826}{1658850077765614801}e^{7} - \frac{641984839627362807043}{1658850077765614801}e^{6} + \frac{939419538862031152139}{1658850077765614801}e^{5} + \frac{696086281214596955610}{1658850077765614801}e^{4} - \frac{873919105649607944915}{1658850077765614801}e^{3} - \frac{416542008039985591582}{1658850077765614801}e^{2} + \frac{313594331749829541304}{1658850077765614801}e + \frac{130584232611818010459}{1658850077765614801}$ |
| 17 | $[17, 17, -w + 8]$ | $\phantom{-}\frac{599288173818499}{1658850077765614801}e^{16} + \frac{24500262446864282}{1658850077765614801}e^{15} - \frac{69519617902387018}{1658850077765614801}e^{14} - \frac{884992248748052314}{1658850077765614801}e^{13} + \frac{1939164184707897611}{1658850077765614801}e^{12} + \frac{12853288748966545289}{1658850077765614801}e^{11} - \frac{23821588747387748740}{1658850077765614801}e^{10} - \frac{97264560911587464345}{1658850077765614801}e^{9} + \frac{149607561762196950572}{1658850077765614801}e^{8} + \frac{415912344134997434768}{1658850077765614801}e^{7} - \frac{488713388425925542623}{1658850077765614801}e^{6} - \frac{1014903378253156901042}{1658850077765614801}e^{5} + \frac{748424432384706586916}{1658850077765614801}e^{4} + \frac{1334569331809647190818}{1658850077765614801}e^{3} - \frac{317764198750045971182}{1658850077765614801}e^{2} - \frac{753444363100399950242}{1658850077765614801}e - \frac{177325061787862376944}{1658850077765614801}$ |
| 19 | $[19, 19, -w - 4]$ | $\phantom{-}\frac{10812510493105646}{1658850077765614801}e^{16} + \frac{287633456422404}{1658850077765614801}e^{15} - \frac{406501622365483040}{1658850077765614801}e^{14} - \frac{49711472079998587}{1658850077765614801}e^{13} + \frac{6205062455841414610}{1658850077765614801}e^{12} + \frac{1491709590995845282}{1658850077765614801}e^{11} - \frac{49760427026776605581}{1658850077765614801}e^{10} - \frac{18823437059309497596}{1658850077765614801}e^{9} + \frac{225867606594118774102}{1658850077765614801}e^{8} + \frac{119356724676075623819}{1658850077765614801}e^{7} - \frac{576819114727743630683}{1658850077765614801}e^{6} - \frac{394632697046718694409}{1658850077765614801}e^{5} + \frac{752954985268811294806}{1658850077765614801}e^{4} + \frac{643476546901583137783}{1658850077765614801}e^{3} - \frac{344490770163282639543}{1658850077765614801}e^{2} - \frac{408871661737904190881}{1658850077765614801}e - \frac{79189387915597098394}{1658850077765614801}$ |
| 19 | $[19, 19, -w + 5]$ | $-\frac{31063922374962691}{1658850077765614801}e^{16} + \frac{21691381260714182}{1658850077765614801}e^{15} + \frac{1161112446887912707}{1658850077765614801}e^{14} - \frac{709720137310625812}{1658850077765614801}e^{13} - \frac{17565367285681291726}{1658850077765614801}e^{12} + \frac{8748072791798200822}{1658850077765614801}e^{11} + \frac{139034359561314555516}{1658850077765614801}e^{10} - \frac{49481416962910966081}{1658850077765614801}e^{9} - \frac{620252172092427006194}{1658850077765614801}e^{8} + \frac{114647358427694629611}{1658850077765614801}e^{7} + \frac{1554041566728929953828}{1658850077765614801}e^{6} + \frac{22719355136113320965}{1658850077765614801}e^{5} - \frac{2014640617248604085318}{1658850077765614801}e^{4} - \frac{489062483065329513489}{1658850077765614801}e^{3} + \frac{1024437739238230752453}{1658850077765614801}e^{2} + \frac{516196273373275005189}{1658850077765614801}e + \frac{45241518028091874439}{1658850077765614801}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{39836611330566597}{1658850077765614801}e^{16} - \frac{13241539409565324}{1658850077765614801}e^{15} - \frac{1499118534936587358}{1658850077765614801}e^{14} + \frac{389620213053314232}{1658850077765614801}e^{13} + \frac{22815344819658767040}{1658850077765614801}e^{12} - \frac{3743961565638176352}{1658850077765614801}e^{11} - \frac{181168077678510695453}{1658850077765614801}e^{10} + \frac{7413580244509456224}{1658850077765614801}e^{9} + \frac{805712528952256428390}{1658850077765614801}e^{8} + \frac{91462501680912481541}{1658850077765614801}e^{7} - \frac{1988250569360964868815}{1658850077765614801}e^{6} - \frac{609475326130547286391}{1658850077765614801}e^{5} + \frac{2474115436743940628208}{1658850077765614801}e^{4} + \frac{1371367404631591130957}{1658850077765614801}e^{3} - \frac{1088361598300691805776}{1658850077765614801}e^{2} - \frac{1027769069588059299835}{1658850077765614801}e - \frac{218754228775973553493}{1658850077765614801}$ |
| 31 | $[31, 31, -6w - 35]$ | $-\frac{49464732354788321}{1658850077765614801}e^{16} + \frac{74790163984209509}{1658850077765614801}e^{15} + \frac{1813004144014165360}{1658850077765614801}e^{14} - \frac{2605212894127103983}{1658850077765614801}e^{13} - \frac{26690136401242723659}{1658850077765614801}e^{12} + \frac{35589350971500710602}{1658850077765614801}e^{11} + \frac{203529358343664609577}{1658850077765614801}e^{10} - \frac{242578207173975523837}{1658850077765614801}e^{9} - \frac{864416020551271124394}{1658850077765614801}e^{8} + \frac{864023851345978374951}{1658850077765614801}e^{7} + \frac{2041733846605414035329}{1658850077765614801}e^{6} - \frac{1504023641930428865026}{1658850077765614801}e^{5} - \frac{2525612468997406194108}{1658850077765614801}e^{4} + \frac{967406895840791109063}{1658850077765614801}e^{3} + \frac{1397948664234522791908}{1658850077765614801}e^{2} + \frac{1151498677695311399}{1658850077765614801}e - \frac{120985430212666415840}{1658850077765614801}$ |
| 31 | $[31, 31, -6w + 41]$ | $-\frac{13632654219000342}{1658850077765614801}e^{16} - \frac{19155268320955344}{1658850077765614801}e^{15} + \frac{537762775871347200}{1658850077765614801}e^{14} + \frac{707519204298936706}{1658850077765614801}e^{13} - \frac{8621123934830070080}{1658850077765614801}e^{12} - \frac{10606532183515646494}{1658850077765614801}e^{11} + \frac{72215277813696043052}{1658850077765614801}e^{10} + \frac{83612249413290722600}{1658850077765614801}e^{9} - \frac{337207593297403216152}{1658850077765614801}e^{8} - \frac{374355984980035979427}{1658850077765614801}e^{7} + \frac{860620547015886821821}{1658850077765614801}e^{6} + \frac{952568126546012639483}{1658850077765614801}e^{5} - \frac{1063373030532813080040}{1658850077765614801}e^{4} - \frac{1277439016452452916140}{1658850077765614801}e^{3} + \frac{383849228408415653397}{1658850077765614801}e^{2} + \frac{696121058002985738115}{1658850077765614801}e + \frac{166029593589537949113}{1658850077765614801}$ |
| 37 | $[37, 37, -w - 1]$ | $\phantom{-}\frac{19929068704112129}{1658850077765614801}e^{16} - \frac{29055846969226359}{1658850077765614801}e^{15} - \frac{719518843480038435}{1658850077765614801}e^{14} + \frac{992243559925186243}{1658850077765614801}e^{13} + \frac{10379646000363882159}{1658850077765614801}e^{12} - \frac{13182476911933047417}{1658850077765614801}e^{11} - \frac{76992300419718321527}{1658850077765614801}e^{10} + \frac{86316458451344108031}{1658850077765614801}e^{9} + \frac{314536709502743251020}{1658850077765614801}e^{8} - \frac{289439222659370121789}{1658850077765614801}e^{7} - \frac{700545163926866747362}{1658850077765614801}e^{6} + \frac{455207432455111379560}{1658850077765614801}e^{5} + \frac{782456125993224555594}{1658850077765614801}e^{4} - \frac{227644814866450969637}{1658850077765614801}e^{3} - \frac{346682135978195855238}{1658850077765614801}e^{2} - \frac{41879651502675667786}{1658850077765614801}e - \frac{6256832122637407750}{1658850077765614801}$ |
| 37 | $[37, 37, w - 2]$ | $-\frac{73318187044809282}{1658850077765614801}e^{16} + \frac{97201372765949956}{1658850077765614801}e^{15} + \frac{2666160507476448369}{1658850077765614801}e^{14} - \frac{3334597928981686964}{1658850077765614801}e^{13} - \frac{38864263117309753187}{1658850077765614801}e^{12} + \frac{44510658545207636499}{1658850077765614801}e^{11} + \frac{292768801287661653628}{1658850077765614801}e^{10} - \frac{292361308261497445117}{1658850077765614801}e^{9} - \frac{1224967571684526276122}{1658850077765614801}e^{8} + \frac{975466497569618069964}{1658850077765614801}e^{7} + \frac{2839387080341518812177}{1658850077765614801}e^{6} - \frac{1468679660053522579051}{1658850077765614801}e^{5} - \frac{3413996628869685523918}{1658850077765614801}e^{4} + \frac{495521429407618990050}{1658850077765614801}e^{3} + \frac{1752477581722959983925}{1658850077765614801}e^{2} + \frac{421344188309434630376}{1658850077765614801}e - \frac{22213796610050096743}{1658850077765614801}$ |
| 47 | $[47, 47, 3w + 16]$ | $-\frac{103046738048310927}{3317700155531229602}e^{16} - \frac{39159053607866014}{1658850077765614801}e^{15} + \frac{2040528693130607750}{1658850077765614801}e^{14} + \frac{3178607266490622149}{3317700155531229602}e^{13} - \frac{33025187391216754332}{1658850077765614801}e^{12} - \frac{53119215582107284195}{3317700155531229602}e^{11} + \frac{563718714633378175699}{3317700155531229602}e^{10} + \frac{471789565944964764325}{3317700155531229602}e^{9} - \frac{1360019305229501540155}{1658850077765614801}e^{8} - \frac{2392190433589941106171}{3317700155531229602}e^{7} + \frac{7317659348335359571839}{3317700155531229602}e^{6} + \frac{6897764301673608765337}{3317700155531229602}e^{5} - \frac{9800113848463042262123}{3317700155531229602}e^{4} - \frac{10482830673730606933337}{3317700155531229602}e^{3} + \frac{2052767422374878639319}{1658850077765614801}e^{2} + \frac{6535325879596747723819}{3317700155531229602}e + \frac{1564971840150307223733}{3317700155531229602}$ |
| 47 | $[47, 47, -3w + 19]$ | $-\frac{7327255183691282}{1658850077765614801}e^{16} + \frac{27318230708396468}{1658850077765614801}e^{15} + \frac{239594191038667301}{1658850077765614801}e^{14} - \frac{1030636969758371313}{1658850077765614801}e^{13} - \frac{2919495789591744546}{1658850077765614801}e^{12} + \frac{15685179985085134374}{1658850077765614801}e^{11} + \frac{15593813373942993266}{1658850077765614801}e^{10} - \frac{124149227049778041615}{1658850077765614801}e^{9} - \frac{25709953110212214313}{1658850077765614801}e^{8} + \frac{548859196307076158255}{1658850077765614801}e^{7} - \frac{68363278166834084025}{1658850077765614801}e^{6} - \frac{1349203482277734353757}{1658850077765614801}e^{5} + \frac{238106252923391264834}{1658850077765614801}e^{4} + \frac{1720209636929288777720}{1658850077765614801}e^{3} - \frac{6166863117411018537}{1658850077765614801}e^{2} - \frac{925372971470503692326}{1658850077765614801}e - \frac{276189944116106647846}{1658850077765614801}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{135377376234096053}{3317700155531229602}e^{16} - \frac{33944522517747365}{3317700155531229602}e^{15} - \frac{5067957637746554645}{3317700155531229602}e^{14} + \frac{430702434095980602}{1658850077765614801}e^{13} + \frac{38355690316813237445}{1658850077765614801}e^{12} - \frac{4856928746855285849}{3317700155531229602}e^{11} - \frac{302980339953220460997}{1658850077765614801}e^{10} - \frac{44665815099822656599}{3317700155531229602}e^{9} + \frac{2682527659326080496081}{3317700155531229602}e^{8} + \frac{329231003817081043898}{1658850077765614801}e^{7} - \frac{6590214319890915036881}{3317700155531229602}e^{6} - \frac{1519541014881500700586}{1658850077765614801}e^{5} + \frac{8124652281876981197029}{3317700155531229602}e^{4} + \frac{3029618500559898067204}{1658850077765614801}e^{3} - \frac{1680885252478744176028}{1658850077765614801}e^{2} - \frac{4300510959676481426471}{3317700155531229602}e - \frac{512693992322677514946}{1658850077765614801}$ |
| 67 | $[67, 67, 3w - 22]$ | $-\frac{13582018327948105}{3317700155531229602}e^{16} + \frac{30988318712448129}{1658850077765614801}e^{15} + \frac{217526751515381201}{1658850077765614801}e^{14} - \frac{2225680137805794975}{3317700155531229602}e^{13} - \frac{2633019858062255713}{1658850077765614801}e^{12} + \frac{31988993079414854179}{3317700155531229602}e^{11} + \frac{29900314786686068749}{3317700155531229602}e^{10} - \frac{237513325578245597797}{3317700155531229602}e^{9} - \frac{39878770184095328776}{1658850077765614801}e^{8} + \frac{980495124707044022043}{3317700155531229602}e^{7} + \frac{92763494927474443431}{3317700155531229602}e^{6} - \frac{2239502093246867183743}{3317700155531229602}e^{5} - \frac{127149536792032337093}{3317700155531229602}e^{4} + \frac{2606405049464362961273}{3317700155531229602}e^{3} + \frac{199212666227130790770}{1658850077765614801}e^{2} - \frac{1191803674307001874381}{3317700155531229602}e - \frac{373557976065852006587}{3317700155531229602}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -3w - 17]$ | $1$ |