Base field \(\Q(\sqrt{113}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13,13,2w + 9]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - 4x^{23} - 31x^{22} + 133x^{21} + 406x^{20} - 1898x^{19} - 2952x^{18} + 15299x^{17} + 13203x^{16} - 77105x^{15} - 38230x^{14} + 253803x^{13} + 74407x^{12} - 552618x^{11} - 102701x^{10} + 786909x^{9} + 109659x^{8} - 704841x^{7} - 95130x^{6} + 364962x^{5} + 58858x^{4} - 90004x^{3} - 18660x^{2} + 5397x + 1223\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 5]$ | $-\frac{1344751644695844}{22238071080932125}e^{23} + \frac{1343935900504273}{5232487313160500}e^{22} + \frac{158858121620385339}{88952284323728500}e^{21} - \frac{747126940120621701}{88952284323728500}e^{20} - \frac{113625576080794507}{5232487313160500}e^{19} + \frac{2612811373445041144}{22238071080932125}e^{18} + \frac{2488069574530132183}{17790456864745700}e^{17} - \frac{4839800093500477487}{5232487313160500}e^{16} - \frac{8940034412665721371}{17790456864745700}e^{15} + \frac{4746154450831315819}{1046497462632100}e^{14} + \frac{3209731015861592049}{3558091372949140}e^{13} - \frac{321720632318625269282}{22238071080932125}e^{12} - \frac{2687358796305384374}{22238071080932125}e^{11} + \frac{541018726218605163539}{17790456864745700}e^{10} - \frac{249308156563266803389}{88952284323728500}e^{9} - \frac{3705704901808562340741}{88952284323728500}e^{8} + \frac{496268670537440027733}{88952284323728500}e^{7} + \frac{636574273762069385109}{17790456864745700}e^{6} - \frac{84701919530172915657}{17790456864745700}e^{5} - \frac{393661608938111441698}{22238071080932125}e^{4} + \frac{154850245144237375521}{88952284323728500}e^{3} + \frac{368649463457736050877}{88952284323728500}e^{2} - \frac{3511590971076443591}{22238071080932125}e - \frac{20465692558062879279}{88952284323728500}$ |
| 7 | $[7, 7, 6w - 35]$ | $-\frac{1119953418434327}{22238071080932125}e^{23} + \frac{286027249371596}{1308121828290125}e^{22} + \frac{34416419730187403}{22238071080932125}e^{21} - \frac{166346217180909927}{22238071080932125}e^{20} - \frac{25678202776495389}{1308121828290125}e^{19} + \frac{2449267492204530352}{22238071080932125}e^{18} + \frac{584661019355814711}{4447614216186425}e^{17} - \frac{1200648469030863224}{1308121828290125}e^{16} - \frac{2140014669641199417}{4447614216186425}e^{15} + \frac{1252375292979744413}{261624365658025}e^{14} + \frac{701629867519732883}{889522843237285}e^{13} - \frac{362461266156468411231}{22238071080932125}e^{12} + \frac{12468689939585416258}{22238071080932125}e^{11} + \frac{162957606531980104203}{4447614216186425}e^{10} - \frac{111300293271379172328}{22238071080932125}e^{9} - \frac{1193486925762792056957}{22238071080932125}e^{8} + \frac{206456810818983238766}{22238071080932125}e^{7} + \frac{218701639984904215423}{4447614216186425}e^{6} - \frac{35205528746024138949}{4447614216186425}e^{5} - \frac{574570737682106158884}{22238071080932125}e^{4} + \frac{64574066926241462092}{22238071080932125}e^{3} + \frac{141972926193420662429}{22238071080932125}e^{2} - \frac{5664452577780263628}{22238071080932125}e - \frac{8133477135389039058}{22238071080932125}$ |
| 7 | $[7, 7, -6w - 29]$ | $-\frac{12018858302895019}{44476142161864250}e^{23} + \frac{1357339679480406}{1308121828290125}e^{22} + \frac{193502917400053408}{22238071080932125}e^{21} - \frac{789200194827361472}{22238071080932125}e^{20} - \frac{310198842026612633}{2616243656580250}e^{19} + \frac{23212963779979867069}{44476142161864250}e^{18} + \frac{3971683663614823851}{4447614216186425}e^{17} - \frac{5674654352979698814}{1308121828290125}e^{16} - \frac{18065306454588472237}{4447614216186425}e^{15} + \frac{5890969081278932168}{261624365658025}e^{14} + \frac{20219600237137897521}{1779045686474570}e^{13} - \frac{1691773866456952414966}{22238071080932125}e^{12} - \frac{831297177399674899049}{44476142161864250}e^{11} + \frac{751725717017466455333}{4447614216186425}e^{10} + \frac{326378062061080198117}{22238071080932125}e^{9} - \frac{5414313292554075946977}{22238071080932125}e^{8} + \frac{35008811978259782276}{22238071080932125}e^{7} + \frac{970002641823037409423}{4447614216186425}e^{6} - \frac{99728741171964513033}{8895228432372850}e^{5} - \frac{4951370987239016921423}{44476142161864250}e^{4} + \frac{139915680215364278012}{22238071080932125}e^{3} + \frac{1182249516149000913413}{44476142161864250}e^{2} - \frac{33000080891037487041}{44476142161864250}e - \frac{66394224511844104801}{44476142161864250}$ |
| 9 | $[9, 3, 3]$ | $-\frac{5207505087726062}{4447614216186425}e^{23} + \frac{2654872194220227}{523248731316050}e^{22} + \frac{306636654614538461}{8895228432372850}e^{21} - \frac{1481111217835718499}{8895228432372850}e^{20} - \frac{218094943110095893}{523248731316050}e^{19} + \frac{10406619640498218262}{4447614216186425}e^{18} + \frac{4722745895658196537}{1779045686474570}e^{17} - \frac{9694659971122830263}{523248731316050}e^{16} - \frac{16539149259785035999}{1779045686474570}e^{15} + \frac{9577049494145755321}{104649746263210}e^{14} + \frac{5446045514215081755}{355809137294914}e^{13} - \frac{1310054805748801032336}{4447614216186425}e^{12} + \frac{19950008916923829198}{4447614216186425}e^{11} + \frac{1113146457705927101501}{1779045686474570}e^{10} - \frac{604067896195955455311}{8895228432372850}e^{9} - \frac{7713582139623671771509}{8895228432372850}e^{8} + \frac{1109573778825417388617}{8895228432372850}e^{7} + \frac{1341024689758694856881}{1779045686474570}e^{6} - \frac{184782926378345464503}{1779045686474570}e^{5} - \frac{1677995049501603487454}{4447614216186425}e^{4} + \frac{335104011348737782879}{8895228432372850}e^{3} + \frac{794740879353760995023}{8895228432372850}e^{2} - \frac{15344005810235116843}{4447614216186425}e - \frac{44739201054478977121}{8895228432372850}$ |
| 11 | $[11, 11, 4w + 19]$ | $-\frac{17312619044675978}{22238071080932125}e^{23} + \frac{4213513422489944}{1308121828290125}e^{22} + \frac{529354358084085467}{22238071080932125}e^{21} - \frac{2391062718915852403}{22238071080932125}e^{20} - \frac{396960937781033571}{1308121828290125}e^{19} + \frac{34254841960872157328}{22238071080932125}e^{18} + \frac{9303345891519133444}{4447614216186425}e^{17} - \frac{16297369103859092886}{1308121828290125}e^{16} - \frac{37292699894702559938}{4447614216186425}e^{15} + \frac{16464857952848412457}{261624365658025}e^{14} + \frac{16914390509598032782}{889522843237285}e^{13} - \frac{4608058303255139885934}{22238071080932125}e^{12} - \frac{414993199417843429263}{22238071080932125}e^{11} + \frac{2001012552967254579717}{4447614216186425}e^{10} - \frac{295054755546931040942}{22238071080932125}e^{9} - \frac{14142602636427407195598}{22238071080932125}e^{8} + \frac{1253503625230797904074}{22238071080932125}e^{7} + \frac{2499393912482775622132}{4447614216186425}e^{6} - \frac{259141602441543184631}{4447614216186425}e^{5} - \frac{6331191752145836827476}{22238071080932125}e^{4} + \frac{526890480879691289263}{22238071080932125}e^{3} + \frac{1510270475071821933106}{22238071080932125}e^{2} - \frac{52303010630486086842}{22238071080932125}e - \frac{85149502708309887062}{22238071080932125}$ |
| 11 | $[11, 11, 4w - 23]$ | $-\frac{4028539198192193}{4447614216186425}e^{23} + \frac{987854968498294}{261624365658025}e^{22} + \frac{122340247671960322}{4447614216186425}e^{21} - \frac{558492642683363548}{4447614216186425}e^{20} - \frac{90928659531683916}{261624365658025}e^{19} + \frac{7967634795921985093}{4447614216186425}e^{18} + \frac{2105527208435013827}{889522843237285}e^{17} - \frac{3773532898115213756}{261624365658025}e^{16} - \frac{8292627525777093178}{889522843237285}e^{15} + \frac{3794204737359939047}{52324873131605}e^{14} + \frac{3644497497723985509}{177904568647457}e^{13} - \frac{1056850520073436950879}{4447614216186425}e^{12} - \frac{80370746782624845748}{4447614216186425}e^{11} + \frac{456866291236166575217}{889522843237285}e^{10} - \frac{88631542877489817377}{4447614216186425}e^{9} - \frac{3216161311391785888548}{4447614216186425}e^{8} + \frac{302693060037208126224}{4447614216186425}e^{7} + \frac{566541758803560376434}{889522843237285}e^{6} - \frac{12051523002272593966}{177904568647457}e^{5} - \frac{1431609409720368521291}{4447614216186425}e^{4} + \frac{120601637755865309043}{4447614216186425}e^{3} + \frac{340922333929532561296}{4447614216186425}e^{2} - \frac{11938686307816752892}{4447614216186425}e - \frac{19211598265872864252}{4447614216186425}$ |
| 13 | $[13, 13, -2w + 11]$ | $\phantom{-}\frac{8472947695926564}{22238071080932125}e^{23} - \frac{2129038959479322}{1308121828290125}e^{22} - \frac{255447649824199971}{22238071080932125}e^{21} + \frac{1207751968311187214}{22238071080932125}e^{20} + \frac{187347140180378123}{1308121828290125}e^{19} - \frac{17302539850364126489}{22238071080932125}e^{18} - \frac{4227525675935464022}{4447614216186425}e^{17} + \frac{8236996278766961718}{1308121828290125}e^{16} + \frac{15744213956672077969}{4447614216186425}e^{15} - \frac{8334448176279921566}{261624365658025}e^{14} - \frac{5911563423037799861}{889522843237285}e^{13} + \frac{2339238769578349994067}{22238071080932125}e^{12} + \frac{25913520565938008769}{22238071080932125}e^{11} - \frac{1020434532371592353046}{4447614216186425}e^{10} + \frac{480920777246022976271}{22238071080932125}e^{9} + \frac{7259806270517581231374}{22238071080932125}e^{8} - \frac{1005433904065846508012}{22238071080932125}e^{7} - \frac{1294302750521801862666}{4447614216186425}e^{6} + \frac{178431272320358122778}{4447614216186425}e^{5} + \frac{3314160907164670158763}{22238071080932125}e^{4} - \frac{336841771624622959269}{22238071080932125}e^{3} - \frac{800143366096578015203}{22238071080932125}e^{2} + \frac{31113428747139340471}{22238071080932125}e + \frac{45379304090922312956}{22238071080932125}$ |
| 13 | $[13, 13, 2w + 9]$ | $-1$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{15237282453472151}{44476142161864250}e^{23} - \frac{4107988801805473}{2616243656580250}e^{22} - \frac{425965331684258189}{44476142161864250}e^{21} + \frac{2244444297461860851}{44476142161864250}e^{20} + \frac{139671499168869841}{1308121828290125}e^{19} - \frac{30771130450831067601}{44476142161864250}e^{18} - \frac{5230733806821597483}{8895228432372850}e^{17} + \frac{13930480570995863287}{2616243656580250}e^{16} + \frac{12853299882304490921}{8895228432372850}e^{15} - \frac{13330210621566324369}{523248731316050}e^{14} + \frac{579219951235253823}{889522843237285}e^{13} + \frac{1762233713224521570289}{22238071080932125}e^{12} - \frac{619956031338421208979}{44476142161864250}e^{11} - \frac{1446332616134865334139}{8895228432372850}e^{10} + \frac{1719166661928183993739}{44476142161864250}e^{9} + \frac{9700624806207251073141}{44476142161864250}e^{8} - \frac{2333807518484137651933}{44476142161864250}e^{7} - \frac{1640816386191173472459}{8895228432372850}e^{6} + \frac{165443852820373457966}{4447614216186425}e^{5} + \frac{4028130766738801466467}{44476142161864250}e^{4} - \frac{534459921529724312421}{44476142161864250}e^{3} - \frac{472753945096436187776}{22238071080932125}e^{2} + \frac{43561872351285388089}{44476142161864250}e + \frac{26647526533565514502}{22238071080932125}$ |
| 31 | $[31, 31, 2w - 13]$ | $-\frac{6826813321044398}{4447614216186425}e^{23} + \frac{3405445138486303}{523248731316050}e^{22} + \frac{408489445823081799}{8895228432372850}e^{21} - \frac{1911212705444743441}{8895228432372850}e^{20} - \frac{297424201205488857}{523248731316050}e^{19} + \frac{13519042535524669323}{4447614216186425}e^{18} + \frac{1336769063884819607}{355809137294914}e^{17} - \frac{12686258516471313787}{523248731316050}e^{16} - \frac{25070252496854382801}{1779045686474570}e^{15} + \frac{12627428432415691609}{104649746263210}e^{14} + \frac{9936175328009036661}{355809137294914}e^{13} - \frac{1740140904240192973119}{4447614216186425}e^{12} - \frac{63207654983969057998}{4447614216186425}e^{11} + \frac{1488532354481423412579}{1779045686474570}e^{10} - \frac{510286526111271290619}{8895228432372850}e^{9} - \frac{10371157508732004411001}{8895228432372850}e^{8} + \frac{1191826049792200413413}{8895228432372850}e^{7} + \frac{1809696867693981070687}{1779045686474570}e^{6} - \frac{215790455807663905693}{1779045686474570}e^{5} - \frac{2268025102988612381586}{4447614216186425}e^{4} + \frac{410506909676424140151}{8895228432372850}e^{3} + \frac{1073655033677423379457}{8895228432372850}e^{2} - \frac{19546815172417958227}{4447614216186425}e - \frac{60371694416389157579}{8895228432372850}$ |
| 31 | $[31, 31, -2w - 11]$ | $\phantom{-}\frac{37442644767472649}{22238071080932125}e^{23} - \frac{18878794237936129}{2616243656580250}e^{22} - \frac{2216089669332915247}{44476142161864250}e^{21} + \frac{10534213655127950923}{44476142161864250}e^{20} + \frac{1589413199793213911}{2616243656580250}e^{19} - \frac{74023727686917026574}{22238071080932125}e^{18} - \frac{34935218869950202499}{8895228432372850}e^{17} + \frac{68955723668364966201}{2616243656580250}e^{16} + \frac{126247042229397855833}{8895228432372850}e^{15} - \frac{68097488383190052587}{523248731316050}e^{14} - \frac{45848277531514159527}{1779045686474570}e^{13} + \frac{9308589910860120554947}{22238071080932125}e^{12} + \frac{96986035904152525454}{22238071080932125}e^{11} - \frac{7899986754101693086747}{8895228432372850}e^{10} + \frac{3475150272382338122047}{44476142161864250}e^{9} + \frac{54646941326338028860993}{44476142161864250}e^{8} - \frac{7028483165898746256459}{44476142161864250}e^{7} - \frac{9478807173283625435267}{8895228432372850}e^{6} + \frac{1212928952629994110431}{8895228432372850}e^{5} + \frac{11829597829101161017533}{22238071080932125}e^{4} - \frac{2247695545052109444583}{44476142161864250}e^{3} - \frac{5588811867578054113771}{44476142161864250}e^{2} + \frac{105085177611465933836}{22238071080932125}e + \frac{314369041853098926417}{44476142161864250}$ |
| 41 | $[41, 41, -8w - 39]$ | $\phantom{-}\frac{308122869560046}{22238071080932125}e^{23} + \frac{398194165510759}{2616243656580250}e^{22} - \frac{69515389060207813}{44476142161864250}e^{21} - \frac{126687252880209633}{44476142161864250}e^{20} + \frac{103953287921209769}{2616243656580250}e^{19} + \frac{119815371014792129}{22238071080932125}e^{18} - \frac{4179956166075422561}{8895228432372850}e^{17} + \frac{688111240674666429}{2616243656580250}e^{16} + \frac{27844757783670800107}{8895228432372850}e^{15} - \frac{1526674546421154373}{523248731316050}e^{14} - \frac{22523464923514432903}{1779045686474570}e^{13} + \frac{327086173422665655013}{22238071080932125}e^{12} + \frac{708674280253598340941}{22238071080932125}e^{11} - \frac{374127786085760640263}{8895228432372850}e^{10} - \frac{2200021087124073308587}{44476142161864250}e^{9} + \frac{3176270350689003640047}{44476142161864250}e^{8} + \frac{2013194916199300950439}{44476142161864250}e^{7} - \frac{629318960016536200953}{8895228432372850}e^{6} - \frac{196087455464867289981}{8895228432372850}e^{5} + \frac{842765885962329569307}{22238071080932125}e^{4} + \frac{198752760135230344943}{44476142161864250}e^{3} - \frac{403459010128929337559}{44476142161864250}e^{2} - \frac{2882903130591663881}{22238071080932125}e + \frac{22074106204723010793}{44476142161864250}$ |
| 41 | $[41, 41, 8w - 47]$ | $-\frac{14983706588686852}{22238071080932125}e^{23} + \frac{4334223597855271}{1308121828290125}e^{22} + \frac{401004528433875403}{22238071080932125}e^{21} - \frac{2362254507553036427}{22238071080932125}e^{20} - \frac{241271766186136614}{1308121828290125}e^{19} + \frac{32313509624576119252}{22238071080932125}e^{18} + \frac{3612044083707079396}{4447614216186425}e^{17} - \frac{14606405774638019699}{1308121828290125}e^{16} - \frac{1163741864343885392}{4447614216186425}e^{15} + \frac{13977363426801122563}{261624365658025}e^{14} - \frac{11664844748538941077}{889522843237285}e^{13} - \frac{3705756634999052595931}{22238071080932125}e^{12} + \frac{1375129864331321579583}{22238071080932125}e^{11} + \frac{1531306283418937046578}{4447614216186425}e^{10} - \frac{3102995256998509395178}{22238071080932125}e^{9} - \frac{10400865424770844061432}{22238071080932125}e^{8} + \frac{3893404067824500078191}{22238071080932125}e^{7} + \frac{1793730188843450766638}{4447614216186425}e^{6} - \frac{529626229604395853029}{4447614216186425}e^{5} - \frac{4521143066872220175884}{22238071080932125}e^{4} + \frac{828283177789071907792}{22238071080932125}e^{3} + \frac{1094475879426457854804}{22238071080932125}e^{2} - \frac{63603957236733553278}{22238071080932125}e - \frac{62415068371283527258}{22238071080932125}$ |
| 53 | $[53, 53, -26w - 125]$ | $\phantom{-}\frac{15202040378935314}{22238071080932125}e^{23} - \frac{7243005968213619}{2616243656580250}e^{22} - \frac{947256741833636717}{44476142161864250}e^{21} + \frac{4152551491265462153}{44476142161864250}e^{20} + \frac{727600486671911171}{2616243656580250}e^{19} - \frac{30081029973715231239}{22238071080932125}e^{18} - \frac{17601176433289532329}{8895228432372850}e^{17} + \frac{28965852832565859361}{2616243656580250}e^{16} + \frac{73806689053680158713}{8895228432372850}e^{15} - \frac{29620503683085055357}{523248731316050}e^{14} - \frac{36152908386286399647}{1779045686474570}e^{13} + \frac{4194248943300310107817}{22238071080932125}e^{12} + \frac{552354639378229886969}{22238071080932125}e^{11} - \frac{3682723655274691801517}{8895228432372850}e^{10} + \frac{5550550720614326417}{44476142161864250}e^{9} + \frac{26277790342038945043323}{44476142161864250}e^{8} - \frac{1830978248276986094249}{44476142161864250}e^{7} - \frac{4679660736138197277147}{8895228432372850}e^{6} + \frac{434454393425612802211}{8895228432372850}e^{5} + \frac{5959022975662208024738}{22238071080932125}e^{4} - \frac{933078867955298684713}{44476142161864250}e^{3} - \frac{2850971505270461191981}{44476142161864250}e^{2} + \frac{47469316748500303871}{22238071080932125}e + \frac{160493299190230262637}{44476142161864250}$ |
| 53 | $[53, 53, 26w - 151]$ | $\phantom{-}\frac{831941538050238}{22238071080932125}e^{23} + \frac{45846003524326}{1308121828290125}e^{22} - \frac{42834367769645482}{22238071080932125}e^{21} - \frac{5578316019102337}{22238071080932125}e^{20} + \frac{50943818609660766}{1308121828290125}e^{19} - \frac{232682625144001963}{22238071080932125}e^{18} - \frac{1870826248818525224}{4447614216186425}e^{17} + \frac{261414542553611381}{1308121828290125}e^{16} + \frac{12135007217586835748}{4447614216186425}e^{15} - \frac{407619504203514672}{261624365658025}e^{14} - \frac{9955318805808962067}{889522843237285}e^{13} + \frac{148080296903276436464}{22238071080932125}e^{12} + \frac{656570015048289553223}{22238071080932125}e^{11} - \frac{74608976083339037257}{4447614216186425}e^{10} - \frac{1103119089266297051168}{22238071080932125}e^{9} + \frac{556384179540577342008}{22238071080932125}e^{8} + \frac{1134821703624283432971}{22238071080932125}e^{7} - \frac{93900348694105829747}{4447614216186425}e^{6} - \frac{131078979259258715074}{4447614216186425}e^{5} + \frac{199640912062684071521}{22238071080932125}e^{4} + \frac{173741033647725481027}{22238071080932125}e^{3} - \frac{32536215835774561876}{22238071080932125}e^{2} - \frac{10208355325692642643}{22238071080932125}e + \frac{1187648087439600977}{22238071080932125}$ |
| 61 | $[61, 61, -14w + 81]$ | $\phantom{-}\frac{117630896119245093}{44476142161864250}e^{23} - \frac{14513097518158757}{1308121828290125}e^{22} - \frac{1777495347851282326}{22238071080932125}e^{21} + \frac{8187713969899199659}{22238071080932125}e^{20} + \frac{2624443741563859901}{2616243656580250}e^{19} - \frac{233053879897005233693}{44476142161864250}e^{18} - \frac{30084180461973641122}{4447614216186425}e^{17} + \frac{55040394941576140208}{1308121828290125}e^{16} + \frac{116554856129357980114}{4447614216186425}e^{15} - \frac{55181920624835424746}{261624365658025}e^{14} - \frac{98971179954930848967}{1779045686474570}e^{13} + \frac{15323796893616876307077}{22238071080932125}e^{12} + \frac{1873440460373944369753}{44476142161864250}e^{11} - \frac{6603635037300290339226}{4447614216186425}e^{10} + \frac{1661208671496199688026}{22238071080932125}e^{9} + \frac{46341211304905675891894}{22238071080932125}e^{8} - \frac{4748286209568509341022}{22238071080932125}e^{7} - \frac{8138199000066282980906}{4447614216186425}e^{6} + \frac{1818887868475776740451}{8895228432372850}e^{5} + \frac{41012241041301605775531}{44476142161864250}e^{4} - \frac{1783027683024281928289}{22238071080932125}e^{3} - \frac{9743764028902240565811}{44476142161864250}e^{2} + \frac{346326856144527585227}{44476142161864250}e + \frac{548661973090292882947}{44476142161864250}$ |
| 61 | $[61, 61, -14w - 67]$ | $\phantom{-}\frac{706358288339129}{4447614216186425}e^{23} - \frac{456013650362199}{523248731316050}e^{22} - \frac{33280907130981497}{8895228432372850}e^{21} + \frac{240455831707154423}{8895228432372850}e^{20} + \frac{14763033528727501}{523248731316050}e^{19} - \frac{1578168370213090854}{4447614216186425}e^{18} - \frac{657159272950823}{1779045686474570}e^{17} + \frac{1356380671959904941}{523248731316050}e^{16} - \frac{2211836950883735927}{1779045686474570}e^{15} - \frac{1222047569480373427}{104649746263210}e^{14} + \frac{2996966434353689529}{355809137294914}e^{13} + \frac{151250524227594670162}{4447614216186425}e^{12} - \frac{124588643395479863261}{4447614216186425}e^{11} - \frac{116250113193185827667}{1779045686474570}e^{10} + \frac{477051807068965328237}{8895228432372850}e^{9} + \frac{738012211112325677133}{8895228432372850}e^{8} - \frac{533962090506081216579}{8895228432372850}e^{7} - \frac{121142121695201903183}{1779045686474570}e^{6} + \frac{65901583187925641203}{1779045686474570}e^{5} + \frac{149806023786796838358}{4447614216186425}e^{4} - \frac{93828237622368473963}{8895228432372850}e^{3} - \frac{73546122028149135921}{8895228432372850}e^{2} + \frac{3223989769060021941}{4447614216186425}e + \frac{4294490805710282347}{8895228432372850}$ |
| 83 | $[83, 83, 2w - 15]$ | $-\frac{7519851961689011}{8895228432372850}e^{23} + \frac{1026528563674164}{261624365658025}e^{22} + \frac{103041917529982952}{4447614216186425}e^{21} - \frac{554873206715869818}{4447614216186425}e^{20} - \frac{130847271685152527}{523248731316050}e^{19} + \frac{15013360904344193011}{8895228432372850}e^{18} + \frac{1149364200419270134}{889522843237285}e^{17} - \frac{3343320734495273141}{261624365658025}e^{16} - \frac{2277364221052433833}{889522843237285}e^{15} + \frac{3136821340517916997}{52324873131605}e^{14} - \frac{1877700895475087659}{355809137294914}e^{13} - \frac{810303185692390361729}{4447614216186425}e^{12} + \frac{374823688873874496769}{8895228432372850}e^{11} + \frac{323801966942191006432}{889522843237285}e^{10} - \frac{462615938894643251377}{4447614216186425}e^{9} - \frac{2109711663141844493138}{4447614216186425}e^{8} + \frac{590289137726505396619}{4447614216186425}e^{7} + \frac{346520423777767702847}{889522843237285}e^{6} - \frac{159474160542021110707}{1779045686474570}e^{5} - \frac{1657023562863787048287}{8895228432372850}e^{4} + \frac{123417452311233877353}{4447614216186425}e^{3} + \frac{381568107711797380447}{8895228432372850}e^{2} - \frac{19511591238829511029}{8895228432372850}e - \frac{21355355269267779519}{8895228432372850}$ |
| 83 | $[83, 83, -2w - 13]$ | $-\frac{75583829636193383}{22238071080932125}e^{23} + \frac{19451382831507884}{1308121828290125}e^{22} + \frac{2218061157079775512}{22238071080932125}e^{21} - \frac{10863501237159792808}{22238071080932125}e^{20} - \frac{1567915777630378031}{1308121828290125}e^{19} + \frac{152870471850291776233}{22238071080932125}e^{18} + \frac{33525466566433269159}{4447614216186425}e^{17} - \frac{71330762900016608996}{1308121828290125}e^{16} - \frac{113828092188889507893}{4447614216186425}e^{15} + \frac{70620962914946121602}{261624365658025}e^{14} + \frac{33221470501790005367}{889522843237285}e^{13} - \frac{19374131731217974553899}{22238071080932125}e^{12} + \frac{797320897512842823107}{22238071080932125}e^{11} + \frac{8259462370356608787437}{4447614216186425}e^{10} - \frac{5419472197714610517862}{22238071080932125}e^{9} - \frac{57478375446621184987953}{22238071080932125}e^{8} + \frac{9342926389571475903314}{22238071080932125}e^{7} + \frac{10044796531040571828352}{4447614216186425}e^{6} - \frac{1521659341741280158341}{4447614216186425}e^{5} - \frac{25294405856177982954361}{22238071080932125}e^{4} + \frac{2723375385033041038018}{22238071080932125}e^{3} + \frac{6031783834426221286791}{22238071080932125}e^{2} - \frac{244140661268314728262}{22238071080932125}e - \frac{340448294072564543057}{22238071080932125}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,2w + 9]$ | $1$ |