Properties

Label 5.5.160801.1-31.1-b
Base field 5.5.160801.1
Weight $[2, 2, 2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{3} - 4w + 2]$
Dimension $21$
CM no
Base change no

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Base field 5.5.160801.1

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[31, 31, w^{3} - 4w + 2]$
Dimension: $21$
CM: no
Base change: no
Newspace dimension: $49$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{21} + 6x^{20} - 24x^{19} - 202x^{18} + 117x^{17} + 2707x^{16} + 1601x^{15} - 18409x^{14} - 23085x^{13} + 65974x^{12} + 121558x^{11} - 109018x^{10} - 317596x^{9} + 9969x^{8} + 399443x^{7} + 196325x^{6} - 165947x^{5} - 178344x^{4} - 44116x^{3} + 6224x^{2} + 3904x + 384\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-\frac{29548229750367949}{19321962557014240}e^{20} - \frac{243516572740723333}{28982943835521360}e^{19} + \frac{1186879711264457353}{28982943835521360}e^{18} + \frac{1392075115019696603}{4830490639253560}e^{17} - \frac{6274013205022930939}{19321962557014240}e^{16} - \frac{76807540826213377681}{19321962557014240}e^{15} - \frac{25298978943760573583}{57965887671042720}e^{14} + \frac{1644506574532610481577}{57965887671042720}e^{13} + \frac{404513212977432984173}{19321962557014240}e^{12} - \frac{323099580244881800963}{2898294383552136}e^{11} - \frac{3750220788162228952883}{28982943835521360}e^{10} + \frac{2243792638581198566419}{9660981278507120}e^{9} + \frac{355394390399697164127}{966098127850712}e^{8} - \frac{11696597836469735102563}{57965887671042720}e^{7} - \frac{29467623378417902281337}{57965887671042720}e^{6} - \frac{2443527260846282460709}{57965887671042720}e^{5} + \frac{15949063631820318897881}{57965887671042720}e^{4} + \frac{256786147687903933283}{1932196255701424}e^{3} - \frac{842132179151694631}{7245735958880340}e^{2} - \frac{17135340241035300112}{1811433989720085}e - \frac{694939020830483196}{603811329906695}$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}\frac{84254629220144273}{57965887671042720}e^{20} + \frac{58103211562875313}{7245735958880340}e^{19} - \frac{561803287673909611}{14491471917760680}e^{18} - \frac{2655720850914606759}{9660981278507120}e^{17} + \frac{5861072759546802951}{19321962557014240}e^{16} + \frac{219619184660587617677}{57965887671042720}e^{15} + \frac{9418814458094695609}{19321962557014240}e^{14} - \frac{1565548523314736074703}{57965887671042720}e^{13} - \frac{1183453908208658567831}{57965887671042720}e^{12} + \frac{51165365209355564349}{483049063925356}e^{11} + \frac{3624129807958227257347}{28982943835521360}e^{10} - \frac{2123815279158146479101}{9660981278507120}e^{9} - \frac{513242338894189061195}{1449147191776068}e^{8} + \frac{10934959379106393310777}{57965887671042720}e^{7} + \frac{28296988356889535481173}{57965887671042720}e^{6} + \frac{863618359186575921617}{19321962557014240}e^{5} - \frac{15267024678075252738529}{57965887671042720}e^{4} - \frac{747877381651716113365}{5796588767104272}e^{3} - \frac{369851104687529901}{1207622659813390}e^{2} + \frac{16631297107884152378}{1811433989720085}e + \frac{682865463464463154}{603811329906695}$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{2729716906879895}{11593177534208544}e^{20} + \frac{7343258268406609}{5796588767104272}e^{19} - \frac{37136073907706255}{5796588767104272}e^{18} - \frac{41956607026213327}{966098127850712}e^{17} + \frac{207732676543256655}{3864392511402848}e^{16} + \frac{6943463739111942275}{11593177534208544}e^{15} + \frac{38732983438249261}{3864392511402848}e^{14} - \frac{49594804377937952021}{11593177534208544}e^{13} - \frac{32031771796893886331}{11593177534208544}e^{12} + \frac{16300641116487023549}{966098127850712}e^{11} + \frac{103253367987140437003}{5796588767104272}e^{10} - \frac{68815024746629154411}{1932196255701424}e^{9} - \frac{148347810113640502997}{2898294383552136}e^{8} + \frac{380273834021741273803}{11593177534208544}e^{7} + \frac{823483777956424432145}{11593177534208544}e^{6} + \frac{7526711267582735491}{3864392511402848}e^{5} - \frac{450160298656034448253}{11593177534208544}e^{4} - \frac{97749878488645051577}{5796588767104272}e^{3} + \frac{58044708152416212}{120762265981339}e^{2} + \frac{441312058535386469}{362286797944017}e + \frac{16102255273760213}{120762265981339}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}\frac{942962039164627}{7245735958880340}e^{20} + \frac{21257999854178329}{28982943835521360}e^{19} - \frac{24587882236235891}{7245735958880340}e^{18} - \frac{121136693391007449}{4830490639253560}e^{17} + \frac{117802569267331473}{4830490639253560}e^{16} + \frac{9974071650814944127}{28982943835521360}e^{15} + \frac{811189167771342399}{9660981278507120}e^{14} - \frac{70550373769476243673}{28982943835521360}e^{13} - \frac{61937125223730475861}{28982943835521360}e^{12} + \frac{18163598881449541089}{1932196255701424}e^{11} + \frac{22711649516628202654}{1811433989720085}e^{10} - \frac{90785470731967766001}{4830490639253560}e^{9} - \frac{101390523521346383527}{2898294383552136}e^{8} + \frac{100167306179604993593}{7245735958880340}e^{7} + \frac{1383510992677489595233}{28982943835521360}e^{6} + \frac{85514916767750475247}{9660981278507120}e^{5} - \frac{729965191656209833619}{28982943835521360}e^{4} - \frac{84625120717342172551}{5796588767104272}e^{3} - \frac{2837626952207754753}{4830490639253560}e^{2} + \frac{3715043908518707197}{3622867979440170}e + \frac{86438209854120183}{603811329906695}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{297730646123698}{603811329906695}e^{20} - \frac{77568801125333327}{28982943835521360}e^{19} + \frac{387173603533172447}{28982943835521360}e^{18} + \frac{888238400388704679}{9660981278507120}e^{17} - \frac{1062987905338372513}{9660981278507120}e^{16} - \frac{3070007506901251073}{2415245319626780}e^{15} - \frac{1927647294651381491}{28982943835521360}e^{14} + \frac{131922750766389771077}{14491471917760680}e^{13} + \frac{60007528329965348661}{9660981278507120}e^{12} - \frac{104290777585897611517}{2898294383552136}e^{11} - \frac{572772699013561301951}{14491471917760680}e^{10} + \frac{45813789644251532191}{603811329906695}e^{9} + \frac{109766190790886922723}{966098127850712}e^{8} - \frac{993425572162249411373}{14491471917760680}e^{7} - \frac{4582998744271112176109}{28982943835521360}e^{6} - \frac{120290707381154226479}{14491471917760680}e^{5} + \frac{2501333923670206111217}{28982943835521360}e^{4} + \frac{38343515555483336459}{966098127850712}e^{3} - \frac{2943079402363814429}{7245735958880340}e^{2} - \frac{10278314176673857951}{3622867979440170}e - \frac{208334094696909144}{603811329906695}$
23 $[23, 23, -w^{2} + 3]$ $-\frac{20544215836027033}{57965887671042720}e^{20} - \frac{28157744363091341}{14491471917760680}e^{19} + \frac{91892626676934239}{9660981278507120}e^{18} + \frac{40265377116179409}{603811329906695}e^{17} - \frac{1466396660948606221}{19321962557014240}e^{16} - \frac{53359148847714932047}{57965887671042720}e^{15} - \frac{5437454741595270727}{57965887671042720}e^{14} + \frac{127054523251376391891}{19321962557014240}e^{13} + \frac{279003097966424618491}{57965887671042720}e^{12} - \frac{149928475933516928903}{5796588767104272}e^{11} - \frac{288932539992949304619}{9660981278507120}e^{10} + \frac{521082423405188218531}{9660981278507120}e^{9} + \frac{30900339223664814838}{362286797944017}e^{8} - \frac{2715709261629786325237}{57965887671042720}e^{7} - \frac{6850099275807440730173}{57965887671042720}e^{6} - \frac{579410855807016209021}{57965887671042720}e^{5} + \frac{1238245029277627045103}{19321962557014240}e^{4} + \frac{45095499645346573913}{1449147191776068}e^{3} + \frac{340773306703582607}{14491471917760680}e^{2} - \frac{1337077204310853901}{603811329906695}e - \frac{165903205563498259}{603811329906695}$
31 $[31, 31, w^{3} - 4w + 2]$ $-1$
32 $[32, 2, 2]$ $-\frac{31685843842828891}{14491471917760680}e^{20} - \frac{174946524236143073}{14491471917760680}e^{19} + \frac{140785553545649853}{2415245319626780}e^{18} + \frac{999733251868435453}{2415245319626780}e^{17} - \frac{2197993657429617947}{4830490639253560}e^{16} - \frac{10336558294248321143}{1811433989720085}e^{15} - \frac{2742946727733438211}{3622867979440170}e^{14} + \frac{49131606158152478383}{1207622659813390}e^{13} + \frac{224196883733963317091}{7245735958880340}e^{12} - \frac{462448258408061802115}{2898294383552136}e^{11} - \frac{114323891294754210827}{603811329906695}e^{10} + \frac{399623490153008232841}{1207622659813390}e^{9} + \frac{777397150058985421765}{1449147191776068}e^{8} - \frac{4096215120121746796999}{14491471917760680}e^{7} - \frac{1340287105573476997222}{1811433989720085}e^{6} - \frac{256264376290471354643}{3622867979440170}e^{5} + \frac{964604000164530478893}{2415245319626780}e^{4} + \frac{571151325055006681201}{2898294383552136}e^{3} + \frac{1189960598578518742}{1811433989720085}e^{2} - \frac{16954354084335174211}{1207622659813390}e - \frac{1040101084965106167}{603811329906695}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{7262141410221103}{28982943835521360}e^{20} + \frac{13222626059185133}{9660981278507120}e^{19} - \frac{24519410577063263}{3622867979440170}e^{18} - \frac{227406284686351479}{4830490639253560}e^{17} + \frac{532170657017385091}{9660981278507120}e^{16} + \frac{9447929033760748331}{14491471917760680}e^{15} + \frac{86272338583581152}{1811433989720085}e^{14} - \frac{8477942738570731778}{1811433989720085}e^{13} - \frac{47517402629214028163}{14491471917760680}e^{12} + \frac{107589202139032274675}{5796588767104272}e^{11} + \frac{300059415809429035717}{14491471917760680}e^{10} - \frac{47504708160805020289}{1207622659813390}e^{9} - \frac{172534154454319870081}{2898294383552136}e^{8} + \frac{347264863943909683629}{9660981278507120}e^{7} + \frac{401525984049120772123}{4830490639253560}e^{6} + \frac{26811691931300684509}{7245735958880340}e^{5} - \frac{663323811899734987847}{14491471917760680}e^{4} - \frac{117886787391980569105}{5796588767104272}e^{3} + \frac{7754415925261799521}{14491471917760680}e^{2} + \frac{2636441161697282386}{1811433989720085}e + \frac{97283653057659613}{603811329906695}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{65462818393417265}{11593177534208544}e^{20} - \frac{90135367169288279}{2898294383552136}e^{19} + \frac{54657507625809461}{362286797944017}e^{18} + \frac{2060580439986620453}{1932196255701424}e^{17} - \frac{4587304157847841507}{3864392511402848}e^{16} - \frac{170478859710479263829}{11593177534208544}e^{15} - \frac{6878499759862513093}{3864392511402848}e^{14} + \frac{1216006481834901038471}{11593177534208544}e^{13} + \frac{910670392804070676371}{11593177534208544}e^{12} - \frac{198890359730032040883}{483049063925356}e^{11} - \frac{2799798480874442474599}{5796588767104272}e^{10} + \frac{1653758672656197651965}{1932196255701424}e^{9} + \frac{993092688632513360729}{724573595888034}e^{8} - \frac{8552756673124569239569}{11593177534208544}e^{7} - \frac{21932020421430423025121}{11593177534208544}e^{6} - \frac{649172360952257007785}{3864392511402848}e^{5} + \frac{11851574144951602309333}{11593177534208544}e^{4} + \frac{2890854061274163480185}{5796588767104272}e^{3} + \frac{155053343097448439}{241524531962678}e^{2} - \frac{25747200503340290533}{724573595888034}e - \frac{526647255829106221}{120762265981339}$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $\phantom{-}\frac{2742630964965335}{11593177534208544}e^{20} + \frac{7743771462675485}{5796588767104272}e^{19} - \frac{5959941876900743}{966098127850712}e^{18} - \frac{88263509603459239}{1932196255701424}e^{17} + \frac{171957598150989829}{3864392511402848}e^{16} + \frac{7271795134164282041}{11593177534208544}e^{15} + \frac{1710422824863281663}{11593177534208544}e^{14} - \frac{17176918127801206681}{3864392511402848}e^{13} - \frac{44300762787513353459}{11593177534208544}e^{12} + \frac{100002157191707090351}{5796588767104272}e^{11} + \frac{43272123740685310735}{1932196255701424}e^{10} - \frac{67647983395900499069}{1932196255701424}e^{9} - \frac{180591918636999229613}{2898294383552136}e^{8} + \frac{320818303766114299343}{11593177534208544}e^{7} + \frac{983447942310553792285}{11593177534208544}e^{6} + \frac{140577103767044158447}{11593177534208544}e^{5} - \frac{173821901617586508791}{3864392511402848}e^{4} - \frac{69635850730300205707}{2898294383552136}e^{3} - \frac{1565072129768060719}{2898294383552136}e^{2} + \frac{413341450413699909}{241524531962678}e + \frac{27206837633414025}{120762265981339}$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}\frac{57112713172953621}{19321962557014240}e^{20} + \frac{117431188940222113}{7245735958880340}e^{19} - \frac{1150160846665580141}{14491471917760680}e^{18} - \frac{5374883786252508049}{9660981278507120}e^{17} + \frac{12259454669749806721}{19321962557014240}e^{16} + \frac{148447145794383112609}{19321962557014240}e^{15} + \frac{43954551835658552477}{57965887671042720}e^{14} - \frac{3183369869525731432033}{57965887671042720}e^{13} - \frac{771767612625043744067}{19321962557014240}e^{12} + \frac{78361097825349697450}{362286797944017}e^{11} + \frac{7201671551515150051217}{28982943835521360}e^{10} - \frac{4370454925168575725331}{9660981278507120}e^{9} - \frac{342401881682616460593}{483049063925356}e^{8} + \frac{23019432087255456646807}{57965887671042720}e^{7} + \frac{56942868773558153789003}{57965887671042720}e^{6} + \frac{4342205222834937453661}{57965887671042720}e^{5} - \frac{30927432324467648024879}{57965887671042720}e^{4} - \frac{492431348164809582245}{1932196255701424}e^{3} + \frac{7042862762430666379}{7245735958880340}e^{2} + \frac{65904330070838594621}{3622867979440170}e + \frac{1321683210893813704}{603811329906695}$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{2415787496138377}{483049063925356}e^{20} + \frac{159188069464371193}{5796588767104272}e^{19} - \frac{776723756464244923}{5796588767104272}e^{18} - \frac{1820393099118797063}{1932196255701424}e^{17} + \frac{2055629017524711441}{1932196255701424}e^{16} + \frac{12557948834949539571}{966098127850712}e^{15} + \frac{8175789548851048645}{5796588767104272}e^{14} - \frac{134468027271301026935}{1449147191776068}e^{13} - \frac{132248024826675437471}{1932196255701424}e^{12} + \frac{264219686342782556011}{724573595888034}e^{11} + \frac{1227726987870931989697}{2898294383552136}e^{10} - \frac{366826023845301741177}{483049063925356}e^{9} - \frac{1164667507479830197221}{966098127850712}e^{8} + \frac{1906024929439313130727}{2898294383552136}e^{7} + \frac{9665328545769725914099}{5796588767104272}e^{6} + \frac{104134369784802843787}{724573595888034}e^{5} - \frac{5232540911372180001019}{5796588767104272}e^{4} - \frac{106151223260126222557}{241524531962678}e^{3} - \frac{598168507125954563}{1449147191776068}e^{2} + \frac{11350401040147277239}{362286797944017}e + \frac{462369081006680032}{120762265981339}$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{34674687343261861}{14491471917760680}e^{20} - \frac{127191387575218057}{9660981278507120}e^{19} + \frac{1852739804122874111}{28982943835521360}e^{18} + \frac{4358699336118146737}{9660981278507120}e^{17} - \frac{4864177377351417899}{9660981278507120}e^{16} - \frac{11259542805853527188}{1811433989720085}e^{15} - \frac{21336920586490866733}{28982943835521360}e^{14} + \frac{160455462611953108409}{3622867979440170}e^{13} + \frac{957793125420636778679}{28982943835521360}e^{12} - \frac{62904635057127580534}{362286797944017}e^{11} - \frac{2943708905108240343083}{14491471917760680}e^{10} + \frac{435241866393171024311}{1207622659813390}e^{9} + \frac{1668480370866142436717}{2898294383552136}e^{8} - \frac{749470649750821271609}{2415245319626780}e^{7} - \frac{7664960295829097872309}{9660981278507120}e^{6} - \frac{126764580370691285039}{1811433989720085}e^{5} + \frac{12410956601305688400341}{28982943835521360}e^{4} + \frac{75529314685480889171}{362286797944017}e^{3} + \frac{492771664227601553}{7245735958880340}e^{2} - \frac{53817844617488569123}{3622867979440170}e - \frac{1091337221368461217}{603811329906695}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{8906390263636509}{4830490639253560}e^{20} + \frac{36782525669498219}{3622867979440170}e^{19} - \frac{714732964997959571}{14491471917760680}e^{18} - \frac{1683173667534308467}{4830490639253560}e^{17} + \frac{939713520982263537}{2415245319626780}e^{16} + \frac{11617168215476881133}{2415245319626780}e^{15} + \frac{8272380435378576443}{14491471917760680}e^{14} - \frac{62235051253736811584}{1811433989720085}e^{13} - \frac{123993313654624065943}{4830490639253560}e^{12} + \frac{391583923638605095319}{2898294383552136}e^{11} + \frac{1146937392828933331853}{7245735958880340}e^{10} - \frac{339961686112644635087}{1207622659813390}e^{9} - \frac{108754777868935293243}{241524531962678}e^{8} + \frac{3529480723180646102353}{14491471917760680}e^{7} + \frac{9029390133379346037977}{14491471917760680}e^{6} + \frac{98998424202071817683}{1811433989720085}e^{5} - \frac{4892524408801234070471}{14491471917760680}e^{4} - \frac{158916261654259515135}{966098127850712}e^{3} - \frac{118865449466034824}{1811433989720085}e^{2} + \frac{21234923180415333238}{1811433989720085}e + \frac{860705792904506729}{603811329906695}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{15063679643941531}{28982943835521360}e^{20} + \frac{27666457548710231}{9660981278507120}e^{19} - \frac{402671833720696633}{28982943835521360}e^{18} - \frac{949215446924252761}{9660981278507120}e^{17} + \frac{264350956936537653}{2415245319626780}e^{16} + \frac{39295789703277527749}{28982943835521360}e^{15} + \frac{2349439181395083037}{14491471917760680}e^{14} - \frac{280620701270615469551}{28982943835521360}e^{13} - \frac{52362866483918212633}{7245735958880340}e^{12} + \frac{55186795728959911205}{1449147191776068}e^{11} + \frac{80596731596249508683}{1811433989720085}e^{10} - \frac{383919812036008923837}{4830490639253560}e^{9} - \frac{366350220646718705263}{2898294383552136}e^{8} + \frac{670454166113061008243}{9660981278507120}e^{7} + \frac{844181672156576341111}{4830490639253560}e^{6} + \frac{399906206347331625667}{28982943835521360}e^{5} - \frac{343524943988989496891}{3622867979440170}e^{4} - \frac{130787183365656904271}{2898294383552136}e^{3} + \frac{1876204252513574831}{7245735958880340}e^{2} + \frac{5810382324025084087}{1811433989720085}e + \frac{237515936200549536}{603811329906695}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{4020605404132143}{2415245319626780}e^{20} - \frac{11038598696784137}{1207622659813390}e^{19} + \frac{26927099679810486}{603811329906695}e^{18} + \frac{1514410183792539013}{4830490639253560}e^{17} - \frac{855286554614529783}{2415245319626780}e^{16} - \frac{20888335435570209029}{4830490639253560}e^{15} - \frac{280902048425575243}{603811329906695}e^{14} + \frac{18633611496824477722}{603811329906695}e^{13} + \frac{109703388966317266017}{4830490639253560}e^{12} - \frac{117142074880563333867}{966098127850712}e^{11} - \frac{84832555918855193726}{603811329906695}e^{10} + \frac{610068717740015221281}{2415245319626780}e^{9} + \frac{96494797992337080963}{241524531962678}e^{8} - \frac{529990554772490603557}{2415245319626780}e^{7} - \frac{666799355606705276559}{1207622659813390}e^{6} - \frac{110644389757786475601}{2415245319626780}e^{5} + \frac{1443790202533318315713}{4830490639253560}e^{4} + \frac{139576127024747488181}{966098127850712}e^{3} - \frac{398996086191899527}{2415245319626780}e^{2} - \frac{6229370233503622529}{603811329906695}e - \frac{759453863878571366}{603811329906695}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-\frac{33678428794798999}{11593177534208544}e^{20} - \frac{30739072152388177}{1932196255701424}e^{19} + \frac{28261222247211074}{362286797944017}e^{18} + \frac{1054649187561330885}{1932196255701424}e^{17} - \frac{2411644226249914713}{3864392511402848}e^{16} - \frac{87318831272666279449}{11593177534208544}e^{15} - \frac{8487957922989121019}{11593177534208544}e^{14} + \frac{623488003873362994163}{11593177534208544}e^{13} + \frac{453317884250700731791}{11593177534208544}e^{12} - \frac{1225714410045282225803}{5796588767104272}e^{11} - \frac{1410141636397069307833}{5796588767104272}e^{10} + \frac{851858674560937945949}{1932196255701424}e^{9} + \frac{2010184906521251963287}{2898294383552136}e^{8} - \frac{1482134452229364645757}{3864392511402848}e^{7} - \frac{3710751258385788926155}{3864392511402848}e^{6} - \frac{921401830422796605223}{11593177534208544}e^{5} + \frac{6032329323796121595721}{11593177534208544}e^{4} + \frac{730911979042431065009}{2898294383552136}e^{3} + \frac{136269609690858067}{2898294383552136}e^{2} - \frac{13029350469191431369}{724573595888034}e - \frac{266272030772909167}{120762265981339}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}\frac{3898728809667571}{966098127850712}e^{20} + \frac{32201455850951387}{1449147191776068}e^{19} - \frac{312577742404849561}{2898294383552136}e^{18} - \frac{368134184474217757}{483049063925356}e^{17} + \frac{410046808034438087}{483049063925356}e^{16} + \frac{10153965402871016551}{966098127850712}e^{15} + \frac{3689334580862471113}{2898294383552136}e^{14} - \frac{54327095440756075121}{724573595888034}e^{13} - \frac{27156367061448365467}{483049063925356}e^{12} + \frac{213249115418312399441}{724573595888034}e^{11} + \frac{501252216501705362131}{1449147191776068}e^{10} - \frac{295330111304062181619}{483049063925356}e^{9} - \frac{237216556097759287325}{241524531962678}e^{8} + \frac{1521398873336990621387}{2898294383552136}e^{7} + \frac{3931320605213026313815}{2898294383552136}e^{6} + \frac{181588405217741815777}{1449147191776068}e^{5} - \frac{265500099863699681318}{362286797944017}e^{4} - \frac{43535529534646840931}{120762265981339}e^{3} - \frac{1799744786502031735}{1449147191776068}e^{2} + \frac{9297860233190486717}{362286797944017}e + \frac{383011832765403217}{120762265981339}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{3} - 4w + 2]$ $1$