Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 8, w + 2]$ |
| Dimension: | $28$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $116$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{28} + 3x^{27} - 41x^{26} - 129x^{25} + 723x^{24} + 2429x^{23} - 7132x^{22} - 26328x^{21} + 42594x^{20} + 181622x^{19} - 152751x^{18} - 832269x^{17} + 279960x^{16} + 2566070x^{15} + 30240x^{14} - 5273306x^{13} - 1380168x^{12} + 6986884x^{11} + 3120350x^{10} - 5569628x^{9} - 3270645x^{8} + 2317403x^{7} + 1614434x^{6} - 363928x^{5} - 279137x^{4} + 20693x^{3} + 11924x^{2} + 916x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{2997482165174731}{11452592201487280}e^{27} - \frac{17012503670511113}{22905184402974560}e^{26} + \frac{62083932937600761}{5726296100743640}e^{25} + \frac{732767609003319747}{22905184402974560}e^{24} - \frac{2222015723416282907}{11452592201487280}e^{23} - \frac{13828634285754255937}{22905184402974560}e^{22} + \frac{130319331048332133}{66584838380740}e^{21} + \frac{37587183222367391027}{5726296100743640}e^{20} - \frac{27794664790578091651}{2290518440297456}e^{19} - \frac{520812231470899229427}{11452592201487280}e^{18} + \frac{134080848173205400691}{2863148050371820}e^{17} + \frac{4802789487967123580611}{22905184402974560}e^{16} - \frac{600764206518569026111}{5726296100743640}e^{15} - \frac{7473184973768859278047}{11452592201487280}e^{14} + \frac{64792888504053837333}{715787012592955}e^{13} + \frac{7792395575584816766487}{5726296100743640}e^{12} + \frac{1798345017311179852857}{11452592201487280}e^{11} - \frac{21168476389207899106787}{11452592201487280}e^{10} - \frac{6229821167820677390347}{11452592201487280}e^{9} + \frac{1104639117765591014551}{715787012592955}e^{8} + \frac{7310398292938938841691}{11452592201487280}e^{7} - \frac{16268438275819793914759}{22905184402974560}e^{6} - \frac{238882164117756005301}{715787012592955}e^{5} + \frac{1693935501277963468317}{11452592201487280}e^{4} + \frac{691473564767684063719}{11452592201487280}e^{3} - \frac{300883586025828775813}{22905184402974560}e^{2} - \frac{25664936676545513543}{11452592201487280}e - \frac{146653010892229161}{2863148050371820}$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}\frac{14599898719150661}{45810368805949120}e^{27} + \frac{42606893846463609}{45810368805949120}e^{26} - \frac{601881991547101297}{45810368805949120}e^{25} - \frac{1832420824136179001}{45810368805949120}e^{24} + \frac{10701521854605067757}{45810368805949120}e^{23} + \frac{34517364118718287651}{45810368805949120}e^{22} - \frac{621946733854607243}{266339353522960}e^{21} - \frac{187216121557947981387}{22905184402974560}e^{20} + \frac{16352653454767210631}{1145259220148728}e^{19} + \frac{646711338390793772023}{11452592201487280}e^{18} - \frac{2464022345222330406329}{45810368805949120}e^{17} - \frac{11886525776841102574853}{45810368805949120}e^{16} + \frac{2611473242683483759491}{22905184402974560}e^{15} + \frac{18417188872232905847461}{22905184402974560}e^{14} - \frac{205988962267657589713}{2863148050371820}e^{13} - \frac{38209002376296324868747}{22905184402974560}e^{12} - \frac{1487724090588570587959}{5726296100743640}e^{11} + \frac{25787713849146273500893}{11452592201487280}e^{10} + \frac{16893464230036117387641}{22905184402974560}e^{9} - \frac{10687045328375122361507}{5726296100743640}e^{8} - \frac{37691668576396213754361}{45810368805949120}e^{7} + \frac{39032569389620638035077}{45810368805949120}e^{6} + \frac{9587779949224568207953}{22905184402974560}e^{5} - \frac{4040189044052698522411}{22905184402974560}e^{4} - \frac{3399259246060966861599}{45810368805949120}e^{3} + \frac{728575217102943397029}{45810368805949120}e^{2} + \frac{60683178435148293189}{22905184402974560}e + \frac{304831816077640023}{5726296100743640}$ |
| 11 | $[11, 11, w + 8]$ | $\phantom{-}\frac{648851975535867}{11452592201487280}e^{27} + \frac{8721670879406967}{45810368805949120}e^{26} - \frac{103419277929696471}{45810368805949120}e^{25} - \frac{186443635000058329}{22905184402974560}e^{24} + \frac{109186821170328641}{2863148050371820}e^{23} + \frac{6966281590322721683}{45810368805949120}e^{22} - \frac{373421137455064291}{1065357414091840}e^{21} - \frac{74680948411507992187}{45810368805949120}e^{20} + \frac{16762109291671132805}{9162073761189824}e^{19} + \frac{507081031071429901641}{45810368805949120}e^{18} - \frac{211296824796807109147}{45810368805949120}e^{17} - \frac{1134675287868568050157}{22905184402974560}e^{16} - \frac{30494832938048561801}{11452592201487280}e^{15} + \frac{3371249128638915319443}{22905184402974560}e^{14} + \frac{1337773398327018355443}{22905184402974560}e^{13} - \frac{6510716302228332926771}{22905184402974560}e^{12} - \frac{2198807821001311336549}{11452592201487280}e^{11} + \frac{7682104995361188134543}{22905184402974560}e^{10} + \frac{912636730123187945211}{2863148050371820}e^{9} - \frac{2350090461563253111107}{11452592201487280}e^{8} - \frac{1613301300117083545801}{5726296100743640}e^{7} + \frac{1249731249113577058481}{45810368805949120}e^{6} + \frac{5198752978535771248713}{45810368805949120}e^{5} + \frac{1087362276965360985609}{45810368805949120}e^{4} - \frac{450094805538712330117}{45810368805949120}e^{3} - \frac{17429776227929037541}{5726296100743640}e^{2} - \frac{2138629614536512159}{11452592201487280}e + \frac{3904768211734737}{2863148050371820}$ |
| 13 | $[13, 13, 4w - 41]$ | $\phantom{-}\frac{223370228127745}{9162073761189824}e^{27} + \frac{822549527879033}{9162073761189824}e^{26} - \frac{1079765237269923}{1145259220148728}e^{25} - \frac{8649518909020115}{2290518440297456}e^{24} + \frac{140216479916850229}{9162073761189824}e^{23} + \frac{634103691391791935}{9162073761189824}e^{22} - \frac{28296090916989177}{213071482818368}e^{21} - \frac{6647822398397108779}{9162073761189824}e^{20} + \frac{5751611248094016445}{9162073761189824}e^{19} + \frac{43999848028962723469}{9162073761189824}e^{18} - \frac{1348770441621747727}{1145259220148728}e^{17} - \frac{47867395321160463799}{2290518440297456}e^{16} - \frac{14951599228936444839}{4581036880594912}e^{15} + \frac{276734038378527301979}{4581036880594912}e^{14} + \frac{119204152796960639809}{4581036880594912}e^{13} - \frac{131316631272632623963}{1145259220148728}e^{12} - \frac{327532184102643825995}{4581036880594912}e^{11} + \frac{316923103438491698447}{2290518440297456}e^{10} + \frac{240095764645450981993}{2290518440297456}e^{9} - \frac{229799463421548346603}{2290518440297456}e^{8} - \frac{771839867180979848249}{9162073761189824}e^{7} + \frac{368316336783405849305}{9162073761189824}e^{6} + \frac{312309177346176675261}{9162073761189824}e^{5} - \frac{75174343266284928121}{9162073761189824}e^{4} - \frac{25706186087441474155}{4581036880594912}e^{3} + \frac{230950605639771853}{286314805037182}e^{2} + \frac{26702840216375244}{143157402518591}e + \frac{1310587901789563}{143157402518591}$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{18589035631183781}{45810368805949120}e^{27} + \frac{55891987335669659}{45810368805949120}e^{26} - \frac{758985658415623467}{45810368805949120}e^{25} - \frac{2394673383875472561}{45810368805949120}e^{24} + \frac{13314019758993631317}{45810368805949120}e^{23} + \frac{44892608968874254541}{45810368805949120}e^{22} - \frac{1516755505799849891}{532678707045920}e^{21} - \frac{120993752520943742551}{11452592201487280}e^{20} + \frac{77172506002872239091}{4581036880594912}e^{19} + \frac{1658205903220931906011}{22905184402974560}e^{18} - \frac{2727468125825061466979}{45810368805949120}e^{17} - \frac{15070127707746242012773}{45810368805949120}e^{16} + \frac{2420533243176086038331}{22905184402974560}e^{15} + \frac{22985371509413087519331}{22905184402974560}e^{14} + \frac{274557995921591430823}{11452592201487280}e^{13} - \frac{46586893797621732174237}{22905184402974560}e^{12} - \frac{3152857273692287607819}{5726296100743640}e^{11} + \frac{15151331421194676807679}{5726296100743640}e^{10} + \frac{27376620035222991035241}{22905184402974560}e^{9} - \frac{11775618286949221093797}{5726296100743640}e^{8} - \frac{55215538371522472020121}{45810368805949120}e^{7} + \frac{37733770226479187745147}{45810368805949120}e^{6} + \frac{3206525488615169264837}{5726296100743640}e^{5} - \frac{1402953618743288453913}{11452592201487280}e^{4} - \frac{3756399061275225080349}{45810368805949120}e^{3} + \frac{438991339402884690089}{45810368805949120}e^{2} + \frac{46501661282748935949}{22905184402974560}e + \frac{240029576387324103}{5726296100743640}$ |
| 19 | $[19, 19, w + 11]$ | $-\frac{1455638169399937}{5726296100743640}e^{27} - \frac{32471519018807679}{45810368805949120}e^{26} + \frac{484735981660285107}{45810368805949120}e^{25} + \frac{701966482481407423}{22905184402974560}e^{24} - \frac{2181342477011304493}{11452592201487280}e^{23} - \frac{26613381625958486091}{45810368805949120}e^{22} + \frac{2061536520934902867}{1065357414091840}e^{21} + \frac{290864794676238543079}{45810368805949120}e^{20} - \frac{110885966760291113693}{9162073761189824}e^{19} - \frac{2027303793349438327037}{45810368805949120}e^{18} + \frac{2163336814231498470199}{45810368805949120}e^{17} + \frac{4705407459246697537739}{22905184402974560}e^{16} - \frac{1230021953563503362123}{11452592201487280}e^{15} - \frac{14747478433973627516191}{22905184402974560}e^{14} + \frac{2194680960186229187489}{22905184402974560}e^{13} + \frac{30953765512096698641447}{22905184402974560}e^{12} + \frac{1807674311207636362053}{11452592201487280}e^{11} - \frac{42187197598091616605051}{22905184402974560}e^{10} - \frac{810922882054294142371}{1431574025185910}e^{9} + \frac{17516325697416020535029}{11452592201487280}e^{8} + \frac{7713305490147235851659}{11452592201487280}e^{7} - \frac{31309728751605889418697}{45810368805949120}e^{6} - \frac{16062479644202804632481}{45810368805949120}e^{5} + \frac{5920391803880592057587}{45810368805949120}e^{4} + \frac{2721965446718859076169}{45810368805949120}e^{3} - \frac{125213127051913217991}{11452592201487280}e^{2} - \frac{22761806807049320707}{11452592201487280}e - \frac{127659265851809239}{2863148050371820}$ |
| 23 | $[23, 23, -2w + 21]$ | $\phantom{-}\frac{2122268602584169}{22905184402974560}e^{27} + \frac{7935054474280121}{22905184402974560}e^{26} - \frac{41247153821058929}{11452592201487280}e^{25} - \frac{169307216384590077}{11452592201487280}e^{24} + \frac{1338827411361418813}{22905184402974560}e^{23} + \frac{6309169153612362479}{22905184402974560}e^{22} - \frac{265737126271507303}{532678707045920}e^{21} - \frac{67374024946450269861}{22905184402974560}e^{20} + \frac{9975312474266805391}{4581036880594912}e^{19} + \frac{454761720283075948063}{22905184402974560}e^{18} - \frac{21244238081377323213}{11452592201487280}e^{17} - \frac{1007927464672948976541}{11452592201487280}e^{16} - \frac{352469161873443248851}{11452592201487280}e^{15} + \frac{2945673521289106664579}{11452592201487280}e^{14} + \frac{2039081054557729569839}{11452592201487280}e^{13} - \frac{2756308617342259746379}{5726296100743640}e^{12} - \frac{5553807241672079086409}{11452592201487280}e^{11} + \frac{3029052532433088058537}{5726296100743640}e^{10} + \frac{2135854483832393168331}{2863148050371820}e^{9} - \frac{1459902576104998211831}{5726296100743640}e^{8} - \frac{14439562222400111391929}{22905184402974560}e^{7} - \frac{1190178696566065480127}{22905184402974560}e^{6} + \frac{5550719035723569194759}{22905184402974560}e^{5} + \frac{1954987825614628286337}{22905184402974560}e^{4} - \frac{11977392769326656583}{715787012592955}e^{3} - \frac{112577663010462786337}{11452592201487280}e^{2} - \frac{4470473056798694677}{5726296100743640}e - \frac{8008091009892159}{1431574025185910}$ |
| 23 | $[23, 23, -2w - 19]$ | $-\frac{6871356318996839}{22905184402974560}e^{27} - \frac{20578078926985481}{22905184402974560}e^{26} + \frac{280417431445469643}{22905184402974560}e^{25} + \frac{881383373708350549}{22905184402974560}e^{24} - \frac{4915359725438943263}{22905184402974560}e^{23} - \frac{16516600300439431159}{22905184402974560}e^{22} + \frac{69911100260789283}{33292419190370}e^{21} + \frac{88984418257033827653}{11452592201487280}e^{20} - \frac{7098813941097549705}{572629610074364}e^{19} - \frac{76167006318156015033}{1431574025185910}e^{18} + \frac{998943009661270374451}{22905184402974560}e^{17} + \frac{5532373983197895295577}{22905184402974560}e^{16} - \frac{873184488109275148829}{11452592201487280}e^{15} - \frac{8426046018545243371469}{11452592201487280}e^{14} - \frac{16863541850855256109}{715787012592955}e^{13} + \frac{17039890252766089476253}{11452592201487280}e^{12} + \frac{2398428335276525714687}{5726296100743640}e^{11} - \frac{5521022004934624346631}{2863148050371820}e^{10} - \frac{10287127842886446871449}{11452592201487280}e^{9} + \frac{1065098053543312106417}{715787012592955}e^{8} + \frac{20628091992526188049979}{22905184402974560}e^{7} - \frac{13427426474761898535233}{22905184402974560}e^{6} - \frac{4759293754543870480117}{11452592201487280}e^{5} + \frac{944820925640812707539}{11452592201487280}e^{4} + \frac{1366351592183752553201}{22905184402974560}e^{3} - \frac{144310414330398408701}{22905184402974560}e^{2} - \frac{15807799677054028841}{11452592201487280}e - \frac{89612457876946667}{2863148050371820}$ |
| 25 | $[25, 5, -5]$ | $-\frac{7870720536058521}{45810368805949120}e^{27} - \frac{23274247053749219}{45810368805949120}e^{26} + \frac{80957960875615033}{11452592201487280}e^{25} + \frac{500102221224086673}{22905184402974560}e^{24} - \frac{5743309336115207037}{45810368805949120}e^{23} - \frac{18824447193217320041}{45810368805949120}e^{22} + \frac{1330684405647544857}{1065357414091840}e^{21} + \frac{204000496381974101459}{45810368805949120}e^{20} - \frac{69639259327294654765}{9162073761189824}e^{19} - \frac{1407862166301744060257}{45810368805949120}e^{18} + \frac{325340534269423213391}{11452592201487280}e^{17} + \frac{3230921495496569862669}{22905184402974560}e^{16} - \frac{1355387352822057226041}{22905184402974560}e^{15} - \frac{10001696403667959920761}{22905184402974560}e^{14} + \frac{759258611417604018839}{22905184402974560}e^{13} + \frac{5184138406841955825733}{5726296100743640}e^{12} + \frac{3400670197451925559361}{22905184402974560}e^{11} - \frac{1750229890653334809861}{1431574025185910}e^{10} - \frac{289568407607772815303}{715787012592955}e^{9} + \frac{11643010030754995725799}{11452592201487280}e^{8} + \frac{20455196501705329302481}{45810368805949120}e^{7} - \frac{21479517000368911177127}{45810368805949120}e^{6} - \frac{10402758938805787759701}{45810368805949120}e^{5} + \frac{4569725296324518915757}{45810368805949120}e^{4} + \frac{940422965837897074267}{22905184402974560}e^{3} - \frac{209239936743076375797}{22905184402974560}e^{2} - \frac{17436883794221192787}{11452592201487280}e - \frac{92647388286461249}{2863148050371820}$ |
| 29 | $[29, 29, 6w - 61]$ | $\phantom{-}\frac{19439587869827279}{45810368805949120}e^{27} + \frac{56048404568623231}{45810368805949120}e^{26} - \frac{100568818890568341}{5726296100743640}e^{25} - \frac{302580370871545943}{5726296100743640}e^{24} + \frac{14364619566846042803}{45810368805949120}e^{23} + \frac{45817673899872222529}{45810368805949120}e^{22} - \frac{3352643755979439583}{1065357414091840}e^{21} - \frac{499713027316015149081}{45810368805949120}e^{20} + \frac{176758153875039750655}{9162073761189824}e^{19} + \frac{3472727659409329459743}{45810368805949120}e^{18} - \frac{415106579502041957707}{5726296100743640}e^{17} - \frac{2006480546845803629899}{5726296100743640}e^{16} + \frac{3436103215950868612619}{22905184402974560}e^{15} + \frac{24993707821115776732089}{22905184402974560}e^{14} - \frac{1588960092709911679181}{22905184402974560}e^{13} - \frac{12983367345237539753197}{5726296100743640}e^{12} - \frac{10273131486380499030769}{22905184402974560}e^{11} + \frac{34796978769295382556877}{11452592201487280}e^{10} + \frac{13557121097548704582967}{11452592201487280}e^{9} - \frac{28007270088697596844991}{11452592201487280}e^{8} - \frac{59456602387932503452079}{45810368805949120}e^{7} + \frac{46790125071685332663223}{45810368805949120}e^{6} + \frac{29239900462110927166299}{45810368805949120}e^{5} - \frac{7343034160673370675363}{45810368805949120}e^{4} - \frac{2221802588657292101633}{22905184402974560}e^{3} + \frac{143660185594425515149}{11452592201487280}e^{2} + \frac{14783355360985867979}{5726296100743640}e + \frac{83730471351592503}{1431574025185910}$ |
| 31 | $[31, 31, w + 12]$ | $\phantom{-}\frac{257942902196437}{715787012592955}e^{27} + \frac{45821122037374417}{45810368805949120}e^{26} - \frac{688396008825711521}{45810368805949120}e^{25} - \frac{988998885022732729}{22905184402974560}e^{24} + \frac{3108651802756465879}{11452592201487280}e^{23} + \frac{37438928539221009853}{45810368805949120}e^{22} - \frac{2957615297463800361}{1065357414091840}e^{21} - \frac{408679222683252995257}{45810368805949120}e^{20} + \frac{161182820671460746991}{9162073761189824}e^{19} + \frac{2846998650045441193851}{45810368805949120}e^{18} - \frac{3233054956686467472717}{45810368805949120}e^{17} - \frac{6614610721546250013637}{22905184402974560}e^{16} + \frac{1971993511695393546619}{11452592201487280}e^{15} + \frac{20816311647528623632053}{22905184402974560}e^{14} - \frac{4779121739426662979727}{22905184402974560}e^{13} - \frac{44142022507761466980581}{22905184402974560}e^{12} - \frac{570804215236973365319}{11452592201487280}e^{11} + \frac{61540536625608850155933}{22905184402974560}e^{10} + \frac{3120393925892739592807}{5726296100743640}e^{9} - \frac{26824846356914650512337}{11452592201487280}e^{8} - \frac{8508716100675929168717}{11452592201487280}e^{7} + \frac{53353359256864827473471}{45810368805949120}e^{6} + \frac{19644842763767297342723}{45810368805949120}e^{5} - \frac{12828780008809376493421}{45810368805949120}e^{4} - \frac{4154193338317303292467}{45810368805949120}e^{3} + \frac{300964494434675129613}{11452592201487280}e^{2} + \frac{45796932348319784201}{11452592201487280}e + \frac{232536776879363757}{2863148050371820}$ |
| 31 | $[31, 31, w + 18]$ | $\phantom{-}\frac{7927693134775869}{45810368805949120}e^{27} + \frac{22900801733451541}{45810368805949120}e^{26} - \frac{327874218441695173}{45810368805949120}e^{25} - \frac{989985459660309209}{45810368805949120}e^{24} + \frac{5845209491096957573}{45810368805949120}e^{23} + \frac{18756850578093774319}{45810368805949120}e^{22} - \frac{170014775877393211}{133169676761480}e^{21} - \frac{102384379255039745853}{22905184402974560}e^{20} + \frac{17813778961084912999}{2290518440297456}e^{19} + \frac{178017714874347510191}{5726296100743640}e^{18} - \frac{1319064843395271560461}{45810368805949120}e^{17} - \frac{6584766382115795299317}{45810368805949120}e^{16} + \frac{1303074012577692031139}{22905184402974560}e^{15} + \frac{10244901573162920518009}{22905184402974560}e^{14} - \frac{71167256886059791599}{5726296100743640}e^{13} - \frac{21220563344941811363383}{22905184402974560}e^{12} - \frac{1266645454516316872481}{5726296100743640}e^{11} + \frac{14099161347777080753387}{11452592201487280}e^{10} + \frac{12371487703381663934769}{22905184402974560}e^{9} - \frac{5554892200851236969083}{5726296100743640}e^{8} - \frac{26424443854569411756449}{45810368805949120}e^{7} + \frac{17490090454638752282713}{45810368805949120}e^{6} + \frac{6317735536393268227107}{22905184402974560}e^{5} - \frac{1083518192062401172549}{22905184402974560}e^{4} - \frac{1745869840235051542251}{45810368805949120}e^{3} + \frac{147551064647563259181}{45810368805949120}e^{2} + \frac{16545954502284524981}{22905184402974560}e + \frac{80359245815197687}{5726296100743640}$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}\frac{9708073747413377}{22905184402974560}e^{27} + \frac{53198440528356921}{45810368805949120}e^{26} - \frac{810695480253168913}{45810368805949120}e^{25} - \frac{287162202449910543}{5726296100743640}e^{24} + \frac{7333150355166622499}{22905184402974560}e^{23} + \frac{43496976684673287209}{45810368805949120}e^{22} - \frac{3495082983871195463}{1065357414091840}e^{21} - \frac{474929313101069746171}{45810368805949120}e^{20} + \frac{190948628455007624745}{9162073761189824}e^{19} + \frac{3308856343093543586333}{45810368805949120}e^{18} - \frac{3843930963352848146741}{45810368805949120}e^{17} - \frac{240195538881870514553}{715787012592955}e^{16} + \frac{147473403506472261892}{715787012592955}e^{15} + \frac{24171670335114036698829}{22905184402974560}e^{14} - \frac{5824572944168716744841}{22905184402974560}e^{13} - \frac{51171566582338196139353}{22905184402974560}e^{12} - \frac{503302157348509791657}{11452592201487280}e^{11} + \frac{71093217933310095399599}{22905184402974560}e^{10} + \frac{7152012616514695529567}{11452592201487280}e^{9} - \frac{30774112876410459029511}{11452592201487280}e^{8} - \frac{19682864818291887904027}{22905184402974560}e^{7} + \frac{60364473391477991606163}{45810368805949120}e^{6} + \frac{22595126528849027133929}{45810368805949120}e^{5} - \frac{14131918708561907737183}{45810368805949120}e^{4} - \frac{4654240133795782821931}{45810368805949120}e^{3} + \frac{653320817760792168923}{22905184402974560}e^{2} + \frac{12582498969795088027}{2863148050371820}e + \frac{128921715674862993}{1431574025185910}$ |
| 37 | $[37, 37, w + 32]$ | $-\frac{2803984879847949}{45810368805949120}e^{27} - \frac{7835862338209761}{45810368805949120}e^{26} + \frac{118097437553025743}{45810368805949120}e^{25} + \frac{341146359380778639}{45810368805949120}e^{24} - \frac{2159573195035551253}{45810368805949120}e^{23} - \frac{6521750059243282739}{45810368805949120}e^{22} + \frac{260862500220559159}{532678707045920}e^{21} + \frac{9004334832090951247}{5726296100743640}e^{20} - \frac{14512999555159178325}{4581036880594912}e^{19} - \frac{254474636668212293899}{22905184402974560}e^{18} + \frac{599659958493877045311}{45810368805949120}e^{17} + \frac{2405777268306675903827}{45810368805949120}e^{16} - \frac{768303902042221199679}{22905184402974560}e^{15} - \frac{3866069516587180770649}{22905184402974560}e^{14} + \frac{525164545404775854903}{11452592201487280}e^{13} + \frac{8416596299122935340213}{22905184402974560}e^{12} - \frac{65525293808698170543}{11452592201487280}e^{11} - \frac{6066278436936574251037}{11452592201487280}e^{10} - \frac{1970985488436099429139}{22905184402974560}e^{9} + \frac{690422690524589673187}{1431574025185910}e^{8} + \frac{6158950505323939339529}{45810368805949120}e^{7} - \frac{11646536127672306734373}{45810368805949120}e^{6} - \frac{487498114564766879373}{5726296100743640}e^{5} + \frac{756006144261512546857}{11452592201487280}e^{4} + \frac{931643250882146201861}{45810368805949120}e^{3} - \frac{290036980696196284171}{45810368805949120}e^{2} - \frac{23421872646902032571}{22905184402974560}e - \frac{166546277340330057}{5726296100743640}$ |
| 41 | $[41, 41, w + 3]$ | $-\frac{3379890565170997}{9162073761189824}e^{27} - \frac{10911476792688465}{9162073761189824}e^{26} + \frac{135714843520883559}{9162073761189824}e^{25} + \frac{465690374429224047}{9162073761189824}e^{24} - \frac{2323330290996047165}{9162073761189824}e^{23} - \frac{8686327238427095395}{9162073761189824}e^{22} + \frac{254663470628672519}{106535741409184}e^{21} + \frac{11627445483259564915}{1145259220148728}e^{20} - \frac{60445283387718319905}{4581036880594912}e^{19} - \frac{315803780331096967763}{4581036880594912}e^{18} + \frac{364177967489358020983}{9162073761189824}e^{17} + \frac{2833237856395066776547}{9162073761189824}e^{16} - \frac{145125529406232099223}{4581036880594912}e^{15} - \frac{4239555764681472253033}{4581036880594912}e^{14} - \frac{490270440631923790033}{2290518440297456}e^{13} + \frac{8338342628910362386077}{4581036880594912}e^{12} + \frac{2009205763679500471749}{2290518440297456}e^{11} - \frac{5149691924201873207729}{2290518440297456}e^{10} - \frac{7092707358098269940707}{4581036880594912}e^{9} + \frac{450751050171727893211}{286314805037182}e^{8} + \frac{12947374960676493532337}{9162073761189824}e^{7} - \frac{4334651836730153424901}{9162073761189824}e^{6} - \frac{684717569904850420607}{1145259220148728}e^{5} - \frac{11724132745284696143}{2290518440297456}e^{4} + \frac{632625644660362100285}{9162073761189824}e^{3} + \frac{32388399873810743413}{9162073761189824}e^{2} - \frac{2610150988234776331}{4581036880594912}e - \frac{30694753775200409}{1145259220148728}$ |
| 41 | $[41, 41, w + 37]$ | $\phantom{-}\frac{1180473779068567}{22905184402974560}e^{27} + \frac{8812017641101621}{45810368805949120}e^{26} - \frac{88602647669991413}{45810368805949120}e^{25} - \frac{91520799361229351}{11452592201487280}e^{24} + \frac{683422745609286089}{22905184402974560}e^{23} + \frac{6597671765796247149}{45810368805949120}e^{22} - \frac{249154494578870143}{1065357414091840}e^{21} - \frac{67552687214288159131}{45810368805949120}e^{20} + \frac{7570894460244257713}{9162073761189824}e^{19} + \frac{431790952736204226053}{45810368805949120}e^{18} + \frac{40967385338503576919}{45810368805949120}e^{17} - \frac{444773301306400196893}{11452592201487280}e^{16} - \frac{125603684781683798449}{5726296100743640}e^{15} + \frac{2343084358329675092089}{22905184402974560}e^{14} + \frac{2270831165166668882199}{22905184402974560}e^{13} - \frac{3717191042137720286173}{22905184402974560}e^{12} - \frac{2684974233605424936437}{11452592201487280}e^{11} + \frac{2885552032834217480639}{22905184402974560}e^{10} + \frac{3606906943065889853277}{11452592201487280}e^{9} + \frac{97101198203618324809}{11452592201487280}e^{8} - \frac{5187967869345824646977}{22905184402974560}e^{7} - \frac{3992093603560202326577}{45810368805949120}e^{6} + \frac{3108700400058159006249}{45810368805949120}e^{5} + \frac{2230136311361171379777}{45810368805949120}e^{4} + \frac{7631945307481176889}{45810368805949120}e^{3} - \frac{117367284193634049267}{22905184402974560}e^{2} - \frac{3692970934421970321}{5726296100743640}e - \frac{11677881184784326}{715787012592955}$ |
| 47 | $[47, 47, w]$ | $-\frac{428833469318459}{1145259220148728}e^{27} - \frac{172659439249461}{143157402518591}e^{26} + \frac{4300506239649969}{286314805037182}e^{25} + \frac{117653179563789853}{2290518440297456}e^{24} - \frac{73571667865766927}{286314805037182}e^{23} - \frac{1094576623287450133}{1145259220148728}e^{22} + \frac{32267806199519563}{13316967676148}e^{21} + \frac{23377352910498511303}{2290518440297456}e^{20} - \frac{7684895639349608593}{572629610074364}e^{19} - \frac{158239644329959756457}{2290518440297456}e^{18} + \frac{23507229026774228491}{572629610074364}e^{17} + \frac{707530569399389018873}{2290518440297456}e^{16} - \frac{43737716463671688147}{1145259220148728}e^{15} - \frac{1055750589586662015697}{1145259220148728}e^{14} - \frac{216021086171475680659}{1145259220148728}e^{13} + \frac{518633866677117405923}{286314805037182}e^{12} + \frac{925964661411695185283}{1145259220148728}e^{11} - \frac{1287682880256808381339}{572629610074364}e^{10} - \frac{410055162823979621791}{286314805037182}e^{9} + \frac{1847514078096415007007}{1145259220148728}e^{8} + \frac{747103784834885874647}{572629610074364}e^{7} - \frac{619124208969092289351}{1145259220148728}e^{6} - \frac{318389754218019318929}{572629610074364}e^{5} + \frac{81717488093383311413}{2290518440297456}e^{4} + \frac{80130188996924714455}{1145259220148728}e^{3} - \frac{2910902996755383521}{2290518440297456}e^{2} - \frac{1181762802920712399}{1145259220148728}e - \frac{6867376433457457}{286314805037182}$ |
| 47 | $[47, 47, w + 46]$ | $-\frac{2497314796770207}{4581036880594912}e^{27} - \frac{956553491067953}{572629610074364}e^{26} + \frac{101729342606331609}{4581036880594912}e^{25} + \frac{82074513368205443}{1145259220148728}e^{24} - \frac{1777406825935675519}{4581036880594912}e^{23} - \frac{3081567351428117987}{2290518440297456}e^{22} + \frac{12563711026453115}{3329241919037}e^{21} + \frac{16634051791150150159}{1145259220148728}e^{20} - \frac{50403924987940712729}{2290518440297456}e^{19} - \frac{114127728846874493069}{1145259220148728}e^{18} + \frac{344173513111881227473}{4581036880594912}e^{17} + \frac{129756472368318073327}{286314805037182}e^{16} - \frac{267764923605469598699}{2290518440297456}e^{15} - \frac{791368959106168523205}{572629610074364}e^{14} - \frac{136551618856424170443}{1145259220148728}e^{13} + \frac{6396715260478151679249}{2290518440297456}e^{12} + \frac{2152662707292714005801}{2290518440297456}e^{11} - \frac{8245273173927783751563}{2290518440297456}e^{10} - \frac{2172654526194478752645}{1145259220148728}e^{9} + \frac{3124532522273475954295}{1145259220148728}e^{8} + \frac{8532740103132813964631}{4581036880594912}e^{7} - \frac{2320793465561774397809}{2290518440297456}e^{6} - \frac{1931573494694226597325}{2290518440297456}e^{5} + \frac{245969838584946292325}{2290518440297456}e^{4} + \frac{517774480714585584717}{4581036880594912}e^{3} - \frac{15372978794809640735}{2290518440297456}e^{2} - \frac{295047223314930623}{143157402518591}e - \frac{7107305895675403}{143157402518591}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |