Base field \(\Q(\sqrt{67}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 67\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7,7,11w + 90]$ |
| Dimension: | $26$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{26} + 4x^{25} - 27x^{24} - 122x^{23} + 294x^{22} + 1600x^{21} - 1581x^{20} - 11844x^{19} + 3504x^{18} + 54568x^{17} + 5659x^{16} - 162688x^{15} - 57722x^{14} + 316500x^{13} + 163747x^{12} - 396810x^{11} - 245311x^{10} + 311748x^{9} + 207793x^{8} - 148016x^{7} - 97388x^{6} + 41190x^{5} + 23977x^{4} - 6232x^{3} - 2755x^{2} + 396x + 107\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -27w + 221]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 8]$ | $\phantom{-}\frac{152390665040}{43828013179}e^{25} + \frac{428407774587}{43828013179}e^{24} - \frac{4592321965740}{43828013179}e^{23} - \frac{13017723644734}{43828013179}e^{22} + \frac{59418568662231}{43828013179}e^{21} + \frac{169750561216018}{43828013179}e^{20} - \frac{7342862468361}{742847681}e^{19} - \frac{1246106626611503}{43828013179}e^{18} + \frac{1962376137358030}{43828013179}e^{17} + \frac{5673477970819307}{43828013179}e^{16} - \frac{5742357171175344}{43828013179}e^{15} - \frac{16639487328328072}{43828013179}e^{14} + \frac{10963660699202090}{43828013179}e^{13} + \frac{31649503108083104}{43828013179}e^{12} - \frac{13575730935556032}{43828013179}e^{11} - \frac{38448935655930179}{43828013179}e^{10} + \frac{10807478249271717}{43828013179}e^{9} + \frac{28809154954148770}{43828013179}e^{8} - \frac{5565483612864226}{43828013179}e^{7} - \frac{12589433185698285}{43828013179}e^{6} + \frac{1884090974033967}{43828013179}e^{5} + \frac{2960024072201707}{43828013179}e^{4} - \frac{376016123749593}{43828013179}e^{3} - \frac{323346196052722}{43828013179}e^{2} + \frac{31348652088814}{43828013179}e + \frac{11241438673199}{43828013179}$ |
| 3 | $[3, 3, -w - 8]$ | $-\frac{330389920703}{87656026358}e^{25} - \frac{893625146231}{87656026358}e^{24} + \frac{5027281767058}{43828013179}e^{23} + \frac{13564847291939}{43828013179}e^{22} - \frac{65969833447394}{43828013179}e^{21} - \frac{176762960097305}{43828013179}e^{20} + \frac{16641620340325}{1485695362}e^{19} + \frac{2594601663695715}{87656026358}e^{18} - \frac{4582866190528781}{87656026358}e^{17} - \frac{11821821936038705}{87656026358}e^{16} + \frac{7010590946163613}{43828013179}e^{15} + \frac{17380500466640612}{43828013179}e^{14} - \frac{14304907050698289}{43828013179}e^{13} - \frac{33259401140019511}{43828013179}e^{12} + \frac{39049205244962003}{87656026358}e^{11} + \frac{81823501005986407}{87656026358}e^{10} - \frac{17728956017993889}{43828013179}e^{9} - \frac{31391027525157788}{43828013179}e^{8} + \frac{21043369603501037}{87656026358}e^{7} + \frac{28581892230571263}{87656026358}e^{6} - \frac{7752678024249845}{87656026358}e^{5} - \frac{7133953664976079}{87656026358}e^{4} + \frac{774556266152696}{43828013179}e^{3} + \frac{424493833937799}{43828013179}e^{2} - \frac{122566979848877}{87656026358}e - \frac{34415354095579}{87656026358}$ |
| 7 | $[7, 7, -11w + 90]$ | $\phantom{-}\frac{124373333619}{43828013179}e^{25} + \frac{334876085041}{43828013179}e^{24} - \frac{3785867143624}{43828013179}e^{23} - \frac{10145740704582}{43828013179}e^{22} + \frac{49745329967443}{43828013179}e^{21} + \frac{131925800873878}{43828013179}e^{20} - \frac{6294251012731}{742847681}e^{19} - \frac{966196198585139}{43828013179}e^{18} + \frac{1744018349647563}{43828013179}e^{17} + \frac{4394269679116909}{43828013179}e^{16} - \frac{5393876943015991}{43828013179}e^{15} - \frac{12907066612688900}{43828013179}e^{14} + \frac{11204023751957133}{43828013179}e^{13} + \frac{24713684449111538}{43828013179}e^{12} - \frac{15711633910981913}{43828013179}e^{11} - \frac{30521696883341933}{43828013179}e^{10} + \frac{14787197071195782}{43828013179}e^{9} + \frac{23661354394489166}{43828013179}e^{8} - \frac{9106599317282270}{43828013179}e^{7} - \frac{10988832228254385}{43828013179}e^{6} + \frac{3435110770952667}{43828013179}e^{5} + \frac{2825755514511441}{43828013179}e^{4} - \frac{690949169911378}{43828013179}e^{3} - \frac{349786237965702}{43828013179}e^{2} + \frac{54466643525704}{43828013179}e + \frac{14840491339991}{43828013179}$ |
| 7 | $[7, 7, -11w - 90]$ | $\phantom{-}1$ |
| 11 | $[11, 11, 6w - 49]$ | $\phantom{-}\frac{269793766086}{43828013179}e^{25} + \frac{724200720527}{43828013179}e^{24} - \frac{8279886061046}{43828013179}e^{23} - \frac{22223150045216}{43828013179}e^{22} + \frac{109501387440758}{43828013179}e^{21} + \frac{293281724371255}{43828013179}e^{20} - \frac{13885270499396}{742847681}e^{19} - \frac{2184466245216112}{43828013179}e^{18} + \frac{3821667202539819}{43828013179}e^{17} + \frac{10121645056207411}{43828013179}e^{16} - \frac{11543204582734033}{43828013179}e^{15} - \frac{30307606761225734}{43828013179}e^{14} + \frac{22703918266336121}{43828013179}e^{13} + \frac{59020538268644875}{43828013179}e^{12} - \frac{28598472552763855}{43828013179}e^{11} - \frac{73458255943980539}{43828013179}e^{10} + \frac{22367227944271716}{43828013179}e^{9} + \frac{56125966322460749}{43828013179}e^{8} - \frac{10627605459504549}{43828013179}e^{7} - \frac{24682040661309154}{43828013179}e^{6} + \frac{3180573574598601}{43828013179}e^{5} + \frac{5738494794700229}{43828013179}e^{4} - \frac{575893863079443}{43828013179}e^{3} - \frac{604797155623430}{43828013179}e^{2} + \frac{46364822694354}{43828013179}e + \frac{19301482590022}{43828013179}$ |
| 11 | $[11, 11, 6w + 49]$ | $-\frac{1804537215}{87656026358}e^{25} + \frac{47571094489}{87656026358}e^{24} + \frac{133997913377}{43828013179}e^{23} - \frac{588278015524}{43828013179}e^{22} - \frac{3462711482889}{43828013179}e^{21} + \frac{5464195478377}{43828013179}e^{20} + \frac{1384156583625}{1485695362}e^{19} - \frac{39494967320541}{87656026358}e^{18} - \frac{540994845125827}{87656026358}e^{17} - \frac{52269017889081}{87656026358}e^{16} + \frac{1082415556140931}{43828013179}e^{15} + \frac{496735318871538}{43828013179}e^{14} - \frac{2650792632161253}{43828013179}e^{13} - \frac{1896143941745205}{43828013179}e^{12} + \frac{7691789997577695}{87656026358}e^{11} + \frac{7132120672910081}{87656026358}e^{10} - \frac{3019468342825351}{43828013179}e^{9} - \frac{3512565068374396}{43828013179}e^{8} + \frac{2076762676001959}{87656026358}e^{7} + \frac{3433275952746465}{87656026358}e^{6} - \frac{105338979545019}{87656026358}e^{5} - \frac{769046394169095}{87656026358}e^{4} - \frac{39531573302867}{43828013179}e^{3} + \frac{31017208031979}{43828013179}e^{2} + \frac{9829791589439}{87656026358}e - \frac{240554497929}{87656026358}$ |
| 17 | $[17, 17, 4w + 33]$ | $-\frac{161002148575}{43828013179}e^{25} - \frac{316555620241}{43828013179}e^{24} + \frac{5335493588525}{43828013179}e^{23} + \frac{10027611689575}{43828013179}e^{22} - \frac{77099636686880}{43828013179}e^{21} - \frac{137283152473564}{43828013179}e^{20} + \frac{10822935511251}{742847681}e^{19} + \frac{1066878946371245}{43828013179}e^{18} - \frac{3347485766970837}{43828013179}e^{17} - \frac{5193484347242365}{43828013179}e^{16} + \frac{11569454406045298}{43828013179}e^{15} + \frac{16475641147308836}{43828013179}e^{14} - \frac{26640056178709857}{43828013179}e^{13} - \frac{34338068393114875}{43828013179}e^{12} + \frac{40467460845954000}{43828013179}e^{11} + \frac{46292765325805561}{43828013179}e^{10} - \frac{39544647102188892}{43828013179}e^{9} - \frac{38867007791949071}{43828013179}e^{8} + \frac{23986067055316185}{43828013179}e^{7} + \frac{19149556301759016}{43828013179}e^{6} - \frac{8607059807983705}{43828013179}e^{5} - \frac{5133466122707278}{43828013179}e^{4} + \frac{1630678243186668}{43828013179}e^{3} + \frac{661306313407484}{43828013179}e^{2} - \frac{121072631047105}{43828013179}e - \frac{30041090369631}{43828013179}$ |
| 17 | $[17, 17, -4w + 33]$ | $-\frac{201103510}{43828013179}e^{25} + \frac{13806844778}{43828013179}e^{24} + \frac{102031355806}{43828013179}e^{23} - \frac{181801611869}{43828013179}e^{22} - \frac{2658935823672}{43828013179}e^{21} - \frac{1292825015016}{43828013179}e^{20} + \frac{492538562908}{742847681}e^{19} + \frac{41067493939348}{43828013179}e^{18} - \frac{167107260857356}{43828013179}e^{17} - \frac{354072646711218}{43828013179}e^{16} + \frac{517923796785444}{43828013179}e^{15} + \frac{1594304301816037}{43828013179}e^{14} - \frac{695565956342652}{43828013179}e^{13} - \frac{4160851312195267}{43828013179}e^{12} - \frac{443239035740612}{43828013179}e^{11} + \frac{6298961231133263}{43828013179}e^{10} + \frac{2784350401324186}{43828013179}e^{9} - \frac{5182512444336654}{43828013179}e^{8} - \frac{3540200402806076}{43828013179}e^{7} + \frac{1999035189031718}{43828013179}e^{6} + \frac{1868436825096898}{43828013179}e^{5} - \frac{256440619066826}{43828013179}e^{4} - \frac{423576962956586}{43828013179}e^{3} - \frac{22184826273398}{43828013179}e^{2} + \frac{32997198352632}{43828013179}e + \frac{4894583691497}{43828013179}$ |
| 25 | $[25, 5, -5]$ | $-\frac{375642114842}{43828013179}e^{25} - \frac{1135664799505}{43828013179}e^{24} + \frac{11021451076920}{43828013179}e^{23} + \frac{34184584254909}{43828013179}e^{22} - \frac{137788784160512}{43828013179}e^{21} - \frac{440755321433719}{43828013179}e^{20} + \frac{16284542188437}{742847681}e^{19} + \frac{3191785384916969}{43828013179}e^{18} - \frac{4102780160577475}{43828013179}e^{17} - \frac{14294335043024153}{43828013179}e^{16} + \frac{11087948494569708}{43828013179}e^{15} + \frac{41088515881058317}{43828013179}e^{14} - \frac{18982887005339714}{43828013179}e^{13} - \frac{76269996961376365}{43828013179}e^{12} + \frac{20260839876058849}{43828013179}e^{11} + \frac{90034567489813327}{43828013179}e^{10} - \frac{13413964543331061}{43828013179}e^{9} - \frac{65384919199175327}{43828013179}e^{8} + \frac{5907825849975018}{43828013179}e^{7} + \frac{27709514225243041}{43828013179}e^{6} - \frac{1995669551832715}{43828013179}e^{5} - \frac{6304038111494910}{43828013179}e^{4} + \frac{450493026926799}{43828013179}e^{3} + \frac{655277711993481}{43828013179}e^{2} - \frac{42298743859893}{43828013179}e - \frac{20375891197710}{43828013179}$ |
| 29 | $[29, 29, -70w + 573]$ | $\phantom{-}\frac{739568617579}{87656026358}e^{25} + \frac{1803382791027}{87656026358}e^{24} - \frac{11649227584072}{43828013179}e^{23} - \frac{27869121042062}{43828013179}e^{22} + \frac{159126637648726}{43828013179}e^{21} + \frac{370993592908044}{43828013179}e^{20} - \frac{42008757638381}{1485695362}e^{19} - \frac{5585350231965825}{87656026358}e^{18} + \frac{12157684494481641}{87656026358}e^{17} + \frac{26221658342240745}{87656026358}e^{16} - \frac{19570103021603014}{43828013179}e^{15} - \frac{39917527372277913}{43828013179}e^{14} + \frac{41809962833210899}{43828013179}e^{13} + \frac{79432319356489951}{43828013179}e^{12} - \frac{117529160038189443}{87656026358}e^{11} - \frac{203477691598360837}{87656026358}e^{10} + \frac{53158730114555493}{43828013179}e^{9} + \frac{80823624949418259}{43828013179}e^{8} - \frac{60255044835944705}{87656026358}e^{7} - \frac{75058928584165151}{87656026358}e^{6} + \frac{20768198149302799}{87656026358}e^{5} + \frac{18822681740581807}{87656026358}e^{4} - \frac{1956459887212432}{43828013179}e^{3} - \frac{1111256029702003}{43828013179}e^{2} + \frac{297466482516045}{87656026358}e + \frac{87964523034711}{87656026358}$ |
| 29 | $[29, 29, 151w - 1236]$ | $-\frac{525657379645}{43828013179}e^{25} - \frac{1451106917057}{43828013179}e^{24} + \frac{15878403845328}{43828013179}e^{23} + \frac{43913087855329}{43828013179}e^{22} - \frac{206458471174761}{43828013179}e^{21} - \frac{569974172081229}{43828013179}e^{20} + \frac{25751123959605}{742847681}e^{19} + \frac{4162824258377918}{43828013179}e^{18} - \frac{6997463879211746}{43828013179}e^{17} - \frac{18853006807397068}{43828013179}e^{16} + \frac{21083832346712642}{43828013179}e^{15} + \frac{55023839448096340}{43828013179}e^{14} - \frac{42338813906871597}{43828013179}e^{13} - \frac{104347478520530006}{43828013179}e^{12} + \frac{57020099914074318}{43828013179}e^{11} + \frac{127038295361796869}{43828013179}e^{10} - \frac{51522615828405556}{43828013179}e^{9} - \frac{96480449858213620}{43828013179}e^{8} + \frac{30830428533108748}{43828013179}e^{7} + \frac{43595259945201056}{43828013179}e^{6} - \frac{11554316098214908}{43828013179}e^{5} - \frac{10855062123418313}{43828013179}e^{4} + \frac{2346504058319729}{43828013179}e^{3} + \frac{1297285221920479}{43828013179}e^{2} - \frac{187565733336379}{43828013179}e - \frac{52970776966768}{43828013179}$ |
| 31 | $[31, 31, -w - 6]$ | $\phantom{-}\frac{315105864834}{43828013179}e^{25} + \frac{814922124820}{43828013179}e^{24} - \frac{9750528541029}{43828013179}e^{23} - \frac{24973579897094}{43828013179}e^{22} + \frac{130469810706135}{43828013179}e^{21} + \frac{329210349921538}{43828013179}e^{20} - \frac{16822372997456}{742847681}e^{19} - \frac{2450526001808358}{43828013179}e^{18} + \frac{4742088457380891}{43828013179}e^{17} + \frac{11357773638570220}{43828013179}e^{16} - \frac{14829459135489666}{43828013179}e^{15} - \frac{34075885058084224}{43828013179}e^{14} + \frac{30704883967381772}{43828013179}e^{13} + \frac{66686296072030294}{43828013179}e^{12} - \frac{41783335400545531}{43828013179}e^{11} - \frac{83844031865183604}{43828013179}e^{10} + \frac{36670716701101090}{43828013179}e^{9} + \frac{65299524235082946}{43828013179}e^{8} - \frac{20330616056507316}{43828013179}e^{7} - \frac{29704859079465438}{43828013179}e^{6} + \frac{6970140878928303}{43828013179}e^{5} + \frac{7285262512108886}{43828013179}e^{4} - \frac{1325917986635900}{43828013179}e^{3} - \frac{836328977814110}{43828013179}e^{2} + \frac{102063315167858}{43828013179}e + \frac{31540535923076}{43828013179}$ |
| 31 | $[31, 31, w - 6]$ | $\phantom{-}\frac{81440667233}{43828013179}e^{25} + \frac{422291609906}{43828013179}e^{24} - \frac{1701213427957}{43828013179}e^{23} - \frac{11962530313114}{43828013179}e^{22} + \frac{9852347684539}{43828013179}e^{21} + \frac{142326553176499}{43828013179}e^{20} + \frac{657341528509}{742847681}e^{19} - \frac{923595212008998}{43828013179}e^{18} - \frac{800904440808270}{43828013179}e^{17} + \frac{3536150104641887}{43828013179}e^{16} + \frac{4615559157393839}{43828013179}e^{15} - \frac{7995718496164292}{43828013179}e^{14} - \frac{14087494939763501}{43828013179}e^{13} + \frac{9820982850974929}{43828013179}e^{12} + \frac{24885239777761104}{43828013179}e^{11} - \frac{4476081809407312}{43828013179}e^{10} - \frac{25398460654887996}{43828013179}e^{9} - \frac{2384598773595940}{43828013179}e^{8} + \frac{14536767905671147}{43828013179}e^{7} + \frac{3229977116988110}{43828013179}e^{6} - \frac{4582460086320612}{43828013179}e^{5} - \frac{1203422108884785}{43828013179}e^{4} + \frac{739294517111650}{43828013179}e^{3} + \frac{182567647924338}{43828013179}e^{2} - \frac{46937798814851}{43828013179}e - \frac{9586589313494}{43828013179}$ |
| 37 | $[37, 37, -21w - 172]$ | $\phantom{-}\frac{186177875221}{43828013179}e^{25} + \frac{528018331128}{43828013179}e^{24} - \frac{5556471078532}{43828013179}e^{23} - \frac{15853558742492}{43828013179}e^{22} + \frac{71280808280486}{43828013179}e^{21} + \frac{203910633378272}{43828013179}e^{20} - \frac{8764675480525}{742847681}e^{19} - \frac{1473859971060457}{43828013179}e^{18} + \frac{2349510878760003}{43828013179}e^{17} + \frac{6597195573321798}{43828013179}e^{16} - \frac{7011000353207664}{43828013179}e^{15} - \frac{19010359805389968}{43828013179}e^{14} + \frac{14085273867491518}{43828013179}e^{13} + \frac{35596906616007697}{43828013179}e^{12} - \frac{19356543731146715}{43828013179}e^{11} - \frac{42924288013285110}{43828013179}e^{10} + \frac{18341628749138388}{43828013179}e^{9} + \frac{32596679424192576}{43828013179}e^{8} - \frac{11716930174951031}{43828013179}e^{7} - \frac{14992456749184126}{43828013179}e^{6} + \frac{4631127695811597}{43828013179}e^{5} + \frac{3867787362297793}{43828013179}e^{4} - \frac{972351850251878}{43828013179}e^{3} - \frac{485945332982364}{43828013179}e^{2} + \frac{79495246483573}{43828013179}e + \frac{21272507828426}{43828013179}$ |
| 37 | $[37, 37, -21w + 172]$ | $-\frac{621505417128}{43828013179}e^{25} - \frac{1836752879114}{43828013179}e^{24} + \frac{18325146250318}{43828013179}e^{23} + \frac{55147460918004}{43828013179}e^{22} - \frac{230959528724232}{43828013179}e^{21} - \frac{708865484813860}{43828013179}e^{20} + \frac{27670451759984}{742847681}e^{19} + \frac{5114953060206668}{43828013179}e^{18} - \frac{7138520534940930}{43828013179}e^{17} - \frac{22815553182712109}{43828013179}e^{16} + \frac{20133599509143508}{43828013179}e^{15} + \frac{65320943760700782}{43828013179}e^{14} - \frac{37317062767566080}{43828013179}e^{13} - \frac{120919728208350659}{43828013179}e^{12} + \frac{46168401039116206}{43828013179}e^{11} + \frac{142971899231864979}{43828013179}e^{10} - \frac{39219057522689124}{43828013179}e^{9} - \frac{105129929621436665}{43828013179}e^{8} + \frac{23338026510806328}{43828013179}e^{7} + \frac{46051923153104610}{43828013179}e^{6} - \frac{9117764019926638}{43828013179}e^{5} - \frac{11125038376180821}{43828013179}e^{4} + \frac{1953098577425340}{43828013179}e^{3} + \frac{1284175531671298}{43828013179}e^{2} - \frac{163371487991694}{43828013179}e - \frac{49815417331991}{43828013179}$ |
| 43 | $[43, 43, 2w - 15]$ | $\phantom{-}\frac{330603076517}{87656026358}e^{25} + \frac{1202610607379}{87656026358}e^{24} - \frac{4539680864868}{43828013179}e^{23} - \frac{18030570520031}{43828013179}e^{22} + \frac{51224134797813}{43828013179}e^{21} + \frac{231391301201295}{43828013179}e^{20} - \frac{10175956243453}{1485695362}e^{19} - \frac{3330828314469661}{87656026358}e^{18} + \frac{1809378523304783}{87656026358}e^{17} + \frac{14784925263701111}{87656026358}e^{16} - \frac{768035893025370}{43828013179}e^{15} - \frac{20944844610191883}{43828013179}e^{14} - \frac{3744872383599301}{43828013179}e^{13} + \frac{37886173723562208}{43828013179}e^{12} + \frac{28259254979634123}{87656026358}e^{11} - \frac{85084356761848389}{87656026358}e^{10} - \frac{21877625333381312}{43828013179}e^{9} + \frac{27898502760522413}{43828013179}e^{8} + \frac{35074762392052349}{87656026358}e^{7} - \frac{19043573858841279}{87656026358}e^{6} - \frac{14363557617752585}{87656026358}e^{5} + \frac{2628063205533731}{87656026358}e^{4} + \frac{1384870679477327}{43828013179}e^{3} + \frac{16724841961063}{43828013179}e^{2} - \frac{193116255502493}{87656026358}e - \frac{24367217444725}{87656026358}$ |
| 43 | $[43, 43, 2w + 15]$ | $\phantom{-}\frac{474481202481}{87656026358}e^{25} + \frac{1137760334237}{87656026358}e^{24} - \frac{7384088635480}{43828013179}e^{23} - \frac{17074441767101}{43828013179}e^{22} + \frac{100165081020907}{43828013179}e^{21} + \frac{219627339467918}{43828013179}e^{20} - \frac{26521166603103}{1485695362}e^{19} - \frac{3178746565763879}{87656026358}e^{18} + \frac{7830189368808879}{87656026358}e^{17} + \frac{14283919488740151}{87656026358}e^{16} - \frac{13208108134222815}{43828013179}e^{15} - \frac{20780944868598666}{43828013179}e^{14} + \frac{30739501964106019}{43828013179}e^{13} + \frac{39763275500037646}{43828013179}e^{12} - \frac{98881387849511779}{87656026358}e^{11} - \frac{100226305285984267}{87656026358}e^{10} + \frac{53715444387143009}{43828013179}e^{9} + \frac{41244327123494715}{43828013179}e^{8} - \frac{74469556250435697}{87656026358}e^{7} - \frac{42885848133519657}{87656026358}e^{6} + \frac{29852278046307327}{87656026358}e^{5} + \frac{12814027549055835}{87656026358}e^{4} - \frac{3025951790248993}{43828013179}e^{3} - \frac{950286221640697}{43828013179}e^{2} + \frac{464366342182949}{87656026358}e + \frac{102024606064283}{87656026358}$ |
| 67 | $[67, 67, -w]$ | $\phantom{-}\frac{925219203432}{43828013179}e^{25} + \frac{2911896767653}{43828013179}e^{24} - \frac{26809413662217}{43828013179}e^{23} - \frac{87645588872522}{43828013179}e^{22} + \frac{329051778828223}{43828013179}e^{21} + \frac{1130042595018128}{43828013179}e^{20} - \frac{37794971971220}{742847681}e^{19} - \frac{8183012332484687}{43828013179}e^{18} + \frac{9082576539773431}{43828013179}e^{17} + \frac{36634975190091761}{43828013179}e^{16} - \frac{22526121304709275}{43828013179}e^{15} - \frac{105169660309228908}{43828013179}e^{14} + \frac{32245638577552241}{43828013179}e^{13} + \frac{194484217927011084}{43828013179}e^{12} - \frac{21265411105453527}{43828013179}e^{11} - \frac{227374557099916011}{43828013179}e^{10} - \frac{2840683536860219}{43828013179}e^{9} + \frac{161430092822018350}{43828013179}e^{8} + \frac{12430555170107102}{43828013179}e^{7} - \frac{65215033513946601}{43828013179}e^{6} - \frac{6193670728427963}{43828013179}e^{5} + \frac{13578925654004945}{43828013179}e^{4} + \frac{1114203139272085}{43828013179}e^{3} - \frac{1179919619051018}{43828013179}e^{2} - \frac{59314151533136}{43828013179}e + \frac{19297631071873}{43828013179}$ |
| 73 | $[73, 73, -3w - 26]$ | $\phantom{-}\frac{1083807161312}{43828013179}e^{25} + \frac{2957021693995}{43828013179}e^{24} - \frac{32995621797486}{43828013179}e^{23} - \frac{90153096764104}{43828013179}e^{22} + \frac{432589272643996}{43828013179}e^{21} + \frac{1180671656386296}{43828013179}e^{20} - \frac{54378151448708}{742847681}e^{19} - \frac{8715669052029067}{43828013179}e^{18} + \frac{14856165885808208}{43828013179}e^{17} + \frac{39971446601290526}{43828013179}e^{16} - \frac{44721849468418072}{43828013179}e^{15} - \frac{118340466771064312}{43828013179}e^{14} + \frac{88506751589742166}{43828013179}e^{13} + \frac{227828435671781703}{43828013179}e^{12} - \frac{114462179280221418}{43828013179}e^{11} - \frac{280962827665479385}{43828013179}e^{10} + \frac{95455136158613684}{43828013179}e^{9} + \frac{214254726771101134}{43828013179}e^{8} - \frac{50918573290000898}{43828013179}e^{7} - \frac{95434944092783852}{43828013179}e^{6} + \frac{17301593401434842}{43828013179}e^{5} + \frac{22902860638600885}{43828013179}e^{4} - \frac{3366516617031218}{43828013179}e^{3} - \frac{2560423523099380}{43828013179}e^{2} + \frac{270689963181006}{43828013179}e + \frac{92479897285302}{43828013179}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7,7,11w + 90]$ | $-1$ |