Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + 9x^{14} + 11x^{13} - 119x^{12} - 357x^{11} + 364x^{10} + 2321x^{9} + 560x^{8} - 6394x^{7} - 4638x^{6} + 8032x^{5} + 7969x^{4} - 3706x^{3} - 4532x^{2} - 122x + 121\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $-\frac{1149312}{38730541}e^{14} - \frac{7184077}{38730541}e^{13} + \frac{14436223}{38730541}e^{12} + \frac{165423074}{38730541}e^{11} + \frac{69266219}{38730541}e^{10} - \frac{1338913939}{38730541}e^{9} - \frac{1645455201}{38730541}e^{8} + \frac{4610167070}{38730541}e^{7} + \frac{7655474852}{38730541}e^{6} - \frac{6888753029}{38730541}e^{5} - \frac{14012738698}{38730541}e^{4} + \frac{3343795565}{38730541}e^{3} + \frac{9183536556}{38730541}e^{2} + \frac{609599068}{38730541}e - \frac{336254426}{38730541}$ |
| 11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{6478798}{38730541}e^{14} + \frac{47609852}{38730541}e^{13} - \frac{4213167}{38730541}e^{12} - \frac{736514880}{38730541}e^{11} - \frac{1057543996}{38730541}e^{10} + \frac{3820615808}{38730541}e^{9} + \frac{7812559839}{38730541}e^{8} - \frac{8972256441}{38730541}e^{7} - \frac{22729602193}{38730541}e^{6} + \frac{9828866711}{38730541}e^{5} + \frac{30196561786}{38730541}e^{4} - \frac{3828563311}{38730541}e^{3} - \frac{15632457265}{38730541}e^{2} - \frac{527508772}{38730541}e + \frac{578461068}{38730541}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $-\frac{4209305}{38730541}e^{14} - \frac{31351880}{38730541}e^{13} - \frac{2365132}{38730541}e^{12} + \frac{464903034}{38730541}e^{11} + \frac{737556412}{38730541}e^{10} - \frac{2210350397}{38730541}e^{9} - \frac{5028290935}{38730541}e^{8} + \frac{4431276384}{38730541}e^{7} + \frac{13305414971}{38730541}e^{6} - \frac{3757335805}{38730541}e^{5} - \frac{15465636833}{38730541}e^{4} + \frac{1347881528}{38730541}e^{3} + \frac{6636828440}{38730541}e^{2} - \frac{630409979}{38730541}e - \frac{250540177}{38730541}$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{4021775}{38730541}e^{14} + \frac{31226025}{38730541}e^{13} + \frac{8127810}{38730541}e^{12} - \frac{466161468}{38730541}e^{11} - \frac{827781584}{38730541}e^{10} + \frac{2228079589}{38730541}e^{9} + \frac{5752887182}{38730541}e^{8} - \frac{4368368014}{38730541}e^{7} - \frac{16067144819}{38730541}e^{6} + \frac{3117216021}{38730541}e^{5} + \frac{20317813783}{38730541}e^{4} + \frac{92512539}{38730541}e^{3} - \frac{9817435739}{38730541}e^{2} - \frac{532448099}{38730541}e + \frac{300617288}{38730541}$ |
| 17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{2813770}{38730541}e^{14} - \frac{20434755}{38730541}e^{13} + \frac{2760889}{38730541}e^{12} + \frac{311854874}{38730541}e^{11} + \frac{428702275}{38730541}e^{10} - \frac{1565637859}{38730541}e^{9} - \frac{3031404482}{38730541}e^{8} + \frac{3427006833}{38730541}e^{7} + \frac{7985337449}{38730541}e^{6} - \frac{3313988033}{38730541}e^{5} - \frac{8915746809}{38730541}e^{4} + \frac{1010872182}{38730541}e^{3} + \frac{3568654330}{38730541}e^{2} + \frac{234629224}{38730541}e - \frac{224188721}{38730541}$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $-\frac{3881433}{38730541}e^{14} - \frac{28122699}{38730541}e^{13} + \frac{1032750}{38730541}e^{12} + \frac{413579383}{38730541}e^{11} + \frac{613201479}{38730541}e^{10} - \frac{1927406960}{38730541}e^{9} - \frac{4097200599}{38730541}e^{8} + \frac{3690728832}{38730541}e^{7} + \frac{10108392637}{38730541}e^{6} - \frac{2850206563}{38730541}e^{5} - \frac{9992166316}{38730541}e^{4} + \frac{1028753663}{38730541}e^{3} + \frac{2742856697}{38730541}e^{2} - \frac{692518215}{38730541}e + \frac{59268219}{38730541}$ |
| 19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $\phantom{-}\frac{4157170}{38730541}e^{14} + \frac{30599200}{38730541}e^{13} - \frac{3552544}{38730541}e^{12} - \frac{484931053}{38730541}e^{11} - \frac{705232774}{38730541}e^{10} + \frac{2581099380}{38730541}e^{9} + \frac{5489815036}{38730541}e^{8} - \frac{5999252862}{38730541}e^{7} - \frac{16647353138}{38730541}e^{6} + \frac{5981267252}{38730541}e^{5} + \frac{22676585465}{38730541}e^{4} - \frac{1800385783}{38730541}e^{3} - \frac{11559720313}{38730541}e^{2} - \frac{197547048}{38730541}e + \frac{152397933}{38730541}$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{11093623}{38730541}e^{14} - \frac{85184009}{38730541}e^{13} - \frac{23012600}{38730541}e^{12} + \frac{1237953834}{38730541}e^{11} + \frac{2214196187}{38730541}e^{10} - \frac{5594979691}{38730541}e^{9} - \frac{14753667597}{38730541}e^{8} + \frac{9783760495}{38730541}e^{7} + \frac{38944055503}{38730541}e^{6} - \frac{4901990310}{38730541}e^{5} - \frac{45712255198}{38730541}e^{4} - \frac{1676551142}{38730541}e^{3} + \frac{20144907143}{38730541}e^{2} + \frac{357017736}{38730541}e - \frac{732134231}{38730541}$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}\frac{422489}{38730541}e^{14} + \frac{6976140}{38730541}e^{13} + \frac{27381786}{38730541}e^{12} - \frac{46324328}{38730541}e^{11} - \frac{454382987}{38730541}e^{10} - \frac{394577216}{38730541}e^{9} + \frac{2012584340}{38730541}e^{8} + \frac{3477315889}{38730541}e^{7} - \frac{2656352415}{38730541}e^{6} - \frac{8124636232}{38730541}e^{5} - \frac{1335538241}{38730541}e^{4} + \frac{5515895686}{38730541}e^{3} + \frac{3340334873}{38730541}e^{2} + \frac{856361955}{38730541}e + \frac{89879071}{38730541}$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{299665}{38730541}e^{14} - \frac{431903}{38730541}e^{13} - \frac{17178502}{38730541}e^{12} - \frac{27716981}{38730541}e^{11} + \frac{170512690}{38730541}e^{10} + \frac{396197785}{38730541}e^{9} - \frac{485502803}{38730541}e^{8} - \frac{1344340550}{38730541}e^{7} + \frac{674995080}{38730541}e^{6} + \frac{1384580022}{38730541}e^{5} - \frac{1254161855}{38730541}e^{4} - \frac{246620783}{38730541}e^{3} + \frac{1377661938}{38730541}e^{2} + \frac{221228000}{38730541}e - \frac{117674591}{38730541}$ |
| 41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{1772671}{38730541}e^{14} + \frac{12781161}{38730541}e^{13} - \frac{3126020}{38730541}e^{12} - \frac{206434076}{38730541}e^{11} - \frac{281505568}{38730541}e^{10} + \frac{1133084400}{38730541}e^{9} + \frac{2296335203}{38730541}e^{8} - \frac{2732396831}{38730541}e^{7} - \frac{7164666175}{38730541}e^{6} + \frac{2741844951}{38730541}e^{5} + \frac{9783473640}{38730541}e^{4} - \frac{380598901}{38730541}e^{3} - \frac{4690413853}{38730541}e^{2} - \frac{789499607}{38730541}e + \frac{47281923}{38730541}$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $-\frac{87270}{38730541}e^{14} - \frac{10913777}{38730541}e^{13} - \frac{81297412}{38730541}e^{12} - \frac{42321182}{38730541}e^{11} + \frac{1057071187}{38730541}e^{10} + \frac{2190289953}{38730541}e^{9} - \frac{3580976680}{38730541}e^{8} - \frac{11956634342}{38730541}e^{7} + \frac{2361119996}{38730541}e^{6} + \frac{23966710602}{38730541}e^{5} + \frac{5801369294}{38730541}e^{4} - \frac{17073482565}{38730541}e^{3} - \frac{6950141563}{38730541}e^{2} + \frac{1021834840}{38730541}e + \frac{239596668}{38730541}$ |
| 59 | $[59, 59, w - 4]$ | $\phantom{-}\frac{5364734}{38730541}e^{14} + \frac{42279285}{38730541}e^{13} + \frac{18114455}{38730541}e^{12} - \frac{597586842}{38730541}e^{11} - \frac{1144156922}{38730541}e^{10} + \frac{2566418544}{38730541}e^{9} + \frac{7201119706}{38730541}e^{8} - \frac{4205213812}{38730541}e^{7} - \frac{17975601276}{38730541}e^{6} + \frac{2227344096}{38730541}e^{5} + \frac{19732829207}{38730541}e^{4} - \frac{520332576}{38730541}e^{3} - \frac{7889126799}{38730541}e^{2} + \frac{1017412964}{38730541}e + \frac{72976851}{38730541}$ |
| 67 | $[67, 67, 2w^{2} - 3w - 8]$ | $-\frac{7371788}{38730541}e^{14} - \frac{58329117}{38730541}e^{13} - \frac{25060976}{38730541}e^{12} + \frac{841466104}{38730541}e^{11} + \frac{1655558377}{38730541}e^{10} - \frac{3670513475}{38730541}e^{9} - \frac{11002165406}{38730541}e^{8} + \frac{5373361548}{38730541}e^{7} + \frac{29101710115}{38730541}e^{6} + \frac{735845112}{38730541}e^{5} - \frac{33894774368}{38730541}e^{4} - \frac{6016576003}{38730541}e^{3} + \frac{14331680040}{38730541}e^{2} + \frac{1908576769}{38730541}e + \frac{16062336}{38730541}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $-\frac{1354107}{38730541}e^{14} - \frac{10980195}{38730541}e^{13} - \frac{18385243}{38730541}e^{12} + \frac{75881193}{38730541}e^{11} + \frac{352494526}{38730541}e^{10} + \frac{424021977}{38730541}e^{9} - \frac{861078914}{38730541}e^{8} - \frac{3500606779}{38730541}e^{7} - \frac{1370483192}{38730541}e^{6} + \frac{7908345180}{38730541}e^{5} + \frac{5791117687}{38730541}e^{4} - \frac{7686174524}{38730541}e^{3} - \frac{4168626447}{38730541}e^{2} + \frac{2936690528}{38730541}e + \frac{93008991}{38730541}$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $\phantom{-}\frac{5464577}{38730541}e^{14} + \frac{35756957}{38730541}e^{13} - \frac{42682052}{38730541}e^{12} - \frac{674882266}{38730541}e^{11} - \frac{462944184}{38730541}e^{10} + \frac{4549245893}{38730541}e^{9} + \frac{5909829667}{38730541}e^{8} - \frac{13658772511}{38730541}e^{7} - \frac{22266949255}{38730541}e^{6} + \frac{18122633460}{38730541}e^{5} + \frac{35290098557}{38730541}e^{4} - \frac{7102819373}{38730541}e^{3} - \frac{20808649996}{38730541}e^{2} - \frac{2436952695}{38730541}e + \frac{434457731}{38730541}$ |
| 97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $-\frac{9000396}{38730541}e^{14} - \frac{72169129}{38730541}e^{13} - \frac{37410441}{38730541}e^{12} + \frac{1025041230}{38730541}e^{11} + \frac{2109003672}{38730541}e^{10} - \frac{4284338465}{38730541}e^{9} - \frac{13630551781}{38730541}e^{8} + \frac{5371362068}{38730541}e^{7} + \frac{34511618026}{38730541}e^{6} + \frac{2848771571}{38730541}e^{5} - \frac{37108640678}{38730541}e^{4} - \frac{6666342392}{38730541}e^{3} + \frac{13924305891}{38730541}e^{2} - \frac{182624699}{38730541}e - \frac{726534299}{38730541}$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{2087045}{38730541}e^{14} + \frac{24332697}{38730541}e^{13} + \frac{92606057}{38730541}e^{12} - \frac{42786305}{38730541}e^{11} - \frac{1334282028}{38730541}e^{10} - \frac{2935082370}{38730541}e^{9} + \frac{3248622398}{38730541}e^{8} + \frac{18034334709}{38730541}e^{7} + \frac{6942807036}{38730541}e^{6} - \frac{37516804863}{38730541}e^{5} - \frac{31384459145}{38730541}e^{4} + \frac{26705760020}{38730541}e^{3} + \frac{27011287897}{38730541}e^{2} - \frac{1041368337}{38730541}e - \frac{387768969}{38730541}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $-1$ |