Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} - w + 3]$ |
| Dimension: | $28$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{28} - 49x^{26} + 1065x^{24} - 13534x^{22} + 111588x^{20} - 626151x^{18} + 2439328x^{16} - 6606928x^{14} + 12256312x^{12} - 15049844x^{10} + 11487528x^{8} - 4854336x^{6} + 906048x^{4} - 58176x^{2} + 1152\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{360775262255}{271810109838144}e^{27} + \frac{5958713165841}{90603369946048}e^{25} - \frac{131155746023537}{90603369946048}e^{23} + \frac{2535993031377407}{135905054919072}e^{21} - \frac{10623775370711515}{67952527459536}e^{19} + \frac{242768142095782985}{271810109838144}e^{17} - \frac{241175593850348951}{67952527459536}e^{15} + \frac{111232992285427293}{11325421243256}e^{13} - \frac{633013500199302355}{33976263729768}e^{11} + \frac{1587990967252602199}{67952527459536}e^{9} - \frac{615497061098849633}{33976263729768}e^{7} + \frac{64799662507086155}{8494065932442}e^{5} - \frac{1872550976843086}{1415677655407}e^{3} + \frac{82346467313608}{1415677655407}e$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{1523499827725}{271810109838144}e^{27} - \frac{24671394836367}{90603369946048}e^{25} + \frac{1593029264874509}{271810109838144}e^{23} - \frac{10009616757869999}{135905054919072}e^{21} + \frac{40739094786562859}{67952527459536}e^{19} - \frac{300327746951182025}{90603369946048}e^{17} + \frac{53911904659584124}{4247032966221}e^{15} - \frac{381642911470975587}{11325421243256}e^{13} + \frac{691186221184888209}{11325421243256}e^{11} - \frac{4943030935169947333}{67952527459536}e^{9} + \frac{1812363416278100729}{33976263729768}e^{7} - \frac{29893721853596082}{1415677655407}e^{5} + \frac{4754147368521793}{1415677655407}e^{3} - \frac{156774589127752}{1415677655407}e$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{93480429539}{67952527459536}e^{26} + \frac{1474144637503}{22650842486512}e^{24} - \frac{92479777686265}{67952527459536}e^{22} + \frac{140854365164125}{8494065932442}e^{20} - \frac{2220090794164927}{16988131864884}e^{18} + \frac{15838600789423071}{22650842486512}e^{16} - \frac{88168172336550763}{33976263729768}e^{14} + \frac{37961058517878883}{5662710621628}e^{12} - \frac{16865367780041606}{1415677655407}e^{10} + \frac{239988979903974737}{16988131864884}e^{8} - \frac{44667861061504646}{4247032966221}e^{6} + \frac{6151111625177223}{1415677655407}e^{4} - \frac{1063466661010322}{1415677655407}e^{2} + \frac{41103643061184}{1415677655407}$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}\frac{836291113883}{271810109838144}e^{27} - \frac{41409658176043}{271810109838144}e^{25} + \frac{909225284490283}{271810109838144}e^{23} - \frac{5832136609735361}{135905054919072}e^{21} + \frac{24241690779245765}{67952527459536}e^{19} - \frac{547561003039873853}{271810109838144}e^{17} + \frac{133804736867784551}{16988131864884}e^{15} - \frac{724776962216233919}{33976263729768}e^{13} + \frac{446025524307899283}{11325421243256}e^{11} - \frac{3251009523233908787}{67952527459536}e^{9} + \frac{405987023604990073}{11325421243256}e^{7} - \frac{62303279613485221}{4247032966221}e^{5} + \frac{3581491860315585}{1415677655407}e^{3} - \frac{154336493960808}{1415677655407}e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{109803990317}{45301684973024}e^{27} + \frac{5564082360317}{45301684973024}e^{25} - \frac{125286800686937}{45301684973024}e^{23} + \frac{826092581383549}{22650842486512}e^{21} - \frac{1769534660372757}{5662710621628}e^{19} + \frac{82638844287611219}{45301684973024}e^{17} - \frac{10472341223333441}{1415677655407}e^{15} + \frac{236126788296196711}{11325421243256}e^{13} - \frac{227469913138706513}{5662710621628}e^{11} + \frac{577172244614172209}{11325421243256}e^{9} - \frac{224634367070690587}{5662710621628}e^{7} + \frac{46693662398185135}{2831355310814}e^{5} - \frac{3760152656259130}{1415677655407}e^{3} + \frac{117018764651142}{1415677655407}e$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-1$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $-\frac{75466191611}{135905054919072}e^{26} + \frac{3230285616295}{135905054919072}e^{24} - \frac{59674842989063}{135905054919072}e^{22} + \frac{311132891429647}{67952527459536}e^{20} - \frac{1004873216617319}{33976263729768}e^{18} + \frac{5531652509117551}{45301684973024}e^{16} - \frac{10880619933693221}{33976263729768}e^{14} + \frac{8675016570123047}{16988131864884}e^{12} - \frac{7592248818937217}{16988131864884}e^{10} + \frac{2027605534826297}{11325421243256}e^{8} - \frac{1419621596374925}{16988131864884}e^{6} + \frac{229624136983946}{1415677655407}e^{4} - \frac{164960034676287}{1415677655407}e^{2} + \frac{16213695724230}{1415677655407}$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-\frac{195669572525}{67952527459536}e^{27} + \frac{3245716055835}{22650842486512}e^{25} - \frac{71692074226547}{22650842486512}e^{23} + \frac{1389382147936673}{33976263729768}e^{21} - \frac{5823128276201917}{16988131864884}e^{19} + \frac{132789061532935883}{67952527459536}e^{17} - \frac{131180084221948391}{16988131864884}e^{15} + \frac{59877063347196437}{2831355310814}e^{13} - \frac{335064692034247597}{8494065932442}e^{11} + \frac{819087446213023783}{16988131864884}e^{9} - \frac{305008945624340393}{8494065932442}e^{7} + \frac{59912853466426693}{4247032966221}e^{5} - \frac{2922701913943966}{1415677655407}e^{3} + \frac{71432278890122}{1415677655407}e$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $-\frac{473767023779}{271810109838144}e^{27} + \frac{23715978572503}{271810109838144}e^{25} - \frac{525502715216951}{271810109838144}e^{23} + \frac{3392975562378835}{135905054919072}e^{21} - \frac{14145087363137399}{67952527459536}e^{19} + \frac{106296331429997159}{90603369946048}e^{17} - \frac{309084397439874827}{67952527459536}e^{15} + \frac{411568170411957311}{33976263729768}e^{13} - \frac{739474292581792847}{33976263729768}e^{11} + \frac{576141292815332993}{22650842486512}e^{9} - \frac{616792135990070225}{33976263729768}e^{7} + \frac{20045842520357637}{2831355310814}e^{5} - \frac{1714720368601662}{1415677655407}e^{3} + \frac{74003262207838}{1415677655407}e$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-\frac{117014672137}{33976263729768}e^{27} + \frac{1456662713975}{8494065932442}e^{25} - \frac{128935679011777}{33976263729768}e^{23} + \frac{835829880868799}{16988131864884}e^{21} - \frac{14093225719966099}{33976263729768}e^{19} + \frac{27018148971519711}{11325421243256}e^{17} - \frac{324436748016135013}{33976263729768}e^{15} + \frac{904928977517592119}{33976263729768}e^{13} - \frac{216451499623560718}{4247032966221}e^{11} + \frac{182748112705688389}{2831355310814}e^{9} - \frac{214692675357389707}{4247032966221}e^{7} + \frac{60803991273664511}{2831355310814}e^{5} - \frac{5255530779858958}{1415677655407}e^{3} + \frac{226471089423884}{1415677655407}e$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $-\frac{516372830029}{135905054919072}e^{27} + \frac{8512371635323}{45301684973024}e^{25} - \frac{560819957433341}{135905054919072}e^{23} + \frac{3605112665463647}{67952527459536}e^{21} - \frac{3764347387641599}{8494065932442}e^{19} + \frac{114316045866457361}{45301684973024}e^{17} - \frac{339504361696553347}{33976263729768}e^{15} + \frac{312048905331954477}{11325421243256}e^{13} - \frac{294931384258872937}{5662710621628}e^{11} + \frac{2211494693650466101}{33976263729768}e^{9} - \frac{852574545458090345}{16988131864884}e^{7} + \frac{58995885648539581}{2831355310814}e^{5} - \frac{4823619317269452}{1415677655407}e^{3} + \frac{158122407712326}{1415677655407}e$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $\phantom{-}\frac{110129284333}{67952527459536}e^{26} - \frac{5479761705391}{67952527459536}e^{24} + \frac{40258539676941}{22650842486512}e^{22} - \frac{194092225759805}{8494065932442}e^{20} + \frac{268839385345250}{1415677655407}e^{18} - \frac{24195773280783601}{22650842486512}e^{16} + \frac{140617803020366903}{33976263729768}e^{14} - \frac{46814003826682159}{4247032966221}e^{12} + \frac{168050607455016887}{8494065932442}e^{10} - \frac{390056306802189497}{16988131864884}e^{8} + \frac{22622209011315978}{1415677655407}e^{6} - \frac{8186411152036638}{1415677655407}e^{4} + \frac{1131015389439638}{1415677655407}e^{2} - \frac{35911143038604}{1415677655407}$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-\frac{141000076165}{67952527459536}e^{26} + \frac{2104724933611}{22650842486512}e^{24} - \frac{123556882941761}{67952527459536}e^{22} + \frac{694102388120789}{33976263729768}e^{20} - \frac{2474312816184485}{16988131864884}e^{18} + \frac{15574778471104209}{22650842486512}e^{16} - \frac{36995256045852877}{16988131864884}e^{14} + \frac{12995663758750291}{2831355310814}e^{12} - \frac{17716099823110065}{2831355310814}e^{10} + \frac{88852514668436797}{16988131864884}e^{8} - \frac{21026033947727921}{8494065932442}e^{6} + \frac{918077604433496}{1415677655407}e^{4} - \frac{196574890553060}{1415677655407}e^{2} + \frac{25008079600892}{1415677655407}$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}\frac{612432689275}{271810109838144}e^{27} - \frac{9981459690921}{90603369946048}e^{25} + \frac{649853195233691}{271810109838144}e^{23} - \frac{4126885019110217}{135905054919072}e^{21} + \frac{17026113452130557}{67952527459536}e^{19} - \frac{127703350709598303}{90603369946048}e^{17} + \frac{23430206029917124}{4247032966221}e^{15} - \frac{170477538071308293}{11325421243256}e^{13} + \frac{319537032816282219}{11325421243256}e^{11} - \frac{2385815105980879531}{67952527459536}e^{9} + \frac{924479823457417055}{33976263729768}e^{7} - \frac{16460251888944686}{1415677655407}e^{5} + \frac{2991576780661339}{1415677655407}e^{3} - \frac{145277129428708}{1415677655407}e$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $-\frac{1254494091935}{135905054919072}e^{27} + \frac{61417238327755}{135905054919072}e^{25} - \frac{1332678823104259}{135905054919072}e^{23} + \frac{8444329058149583}{67952527459536}e^{21} - \frac{34659794490260117}{33976263729768}e^{19} + \frac{772786966538351753}{135905054919072}e^{17} - \frac{745226092583546837}{33976263729768}e^{15} + \frac{248639587604209463}{4247032966221}e^{13} - \frac{601810563273212113}{5662710621628}e^{11} + \frac{4291677252108413951}{33976263729768}e^{9} - \frac{518660477964446279}{5662710621628}e^{7} + \frac{150112919987389004}{4247032966221}e^{5} - \frac{7520944382108622}{1415677655407}e^{3} + \frac{219803209222078}{1415677655407}e$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $-\frac{857013730315}{45301684973024}e^{27} + \frac{126121478994529}{135905054919072}e^{25} - \frac{2744283972966565}{135905054919072}e^{23} + \frac{5818632355165415}{22650842486512}e^{21} - \frac{9003684458351264}{4247032966221}e^{19} + \frac{539244065276107813}{45301684973024}e^{17} - \frac{131300056397647247}{2831355310814}e^{15} + \frac{4262428781962597333}{33976263729768}e^{13} - \frac{3939241163085301181}{16988131864884}e^{11} + \frac{9590299877117534749}{33976263729768}e^{9} - \frac{3586967457708767491}{16988131864884}e^{7} + \frac{240239349210445991}{2831355310814}e^{5} - \frac{19179984062335196}{1415677655407}e^{3} + \frac{688804126693066}{1415677655407}e$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $\phantom{-}\frac{582675733493}{135905054919072}e^{26} - \frac{9333780248511}{45301684973024}e^{24} + \frac{594194694869365}{135905054919072}e^{22} - \frac{3664856493327127}{67952527459536}e^{20} + \frac{14556053229720805}{33976263729768}e^{18} - \frac{103900501433751169}{45301684973024}e^{16} + \frac{142963791870817531}{16988131864884}e^{14} - \frac{59762397828639147}{2831355310814}e^{12} + \frac{200814195261255053}{5662710621628}e^{10} - \frac{1302292438148040485}{33976263729768}e^{8} + \frac{422505145958501365}{16988131864884}e^{6} - \frac{12177119382228940}{1415677655407}e^{4} + \frac{1804155632870929}{1415677655407}e^{2} - \frac{71491701217212}{1415677655407}$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{66145352391}{22650842486512}e^{26} - \frac{8735925779137}{67952527459536}e^{24} + \frac{166901012990665}{67952527459536}e^{22} - \frac{301845029085651}{11325421243256}e^{20} + \frac{3061510910291845}{16988131864884}e^{18} - \frac{17681825942980401}{22650842486512}e^{16} + \frac{11996817689071129}{5662710621628}e^{14} - \frac{27224722195819733}{8494065932442}e^{12} + \frac{5287185441988072}{4247032966221}e^{10} + \frac{70683826991767667}{16988131864884}e^{8} - \frac{62409396608157131}{8494065932442}e^{6} + \frac{6612940147023678}{1415677655407}e^{4} - \frac{1468674592003944}{1415677655407}e^{2} + \frac{74415709259502}{1415677655407}$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $\phantom{-}\frac{911099424491}{271810109838144}e^{27} - \frac{14771702018049}{90603369946048}e^{25} + \frac{956089940557411}{271810109838144}e^{23} - \frac{6031642689022357}{135905054919072}e^{21} + \frac{24700078416780169}{67952527459536}e^{19} - \frac{183711268966309999}{90603369946048}e^{17} + \frac{267079435267411297}{33976263729768}e^{15} - \frac{240225784532140225}{11325421243256}e^{13} + \frac{444354964224789551}{11325421243256}e^{11} - \frac{3264181472626312811}{67952527459536}e^{9} + \frac{1239130862841823951}{33976263729768}e^{7} - \frac{21501887560726596}{1415677655407}e^{5} + \frac{3775074996674111}{1415677655407}e^{3} - \frac{150935373188588}{1415677655407}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} - w + 3]$ | $1$ |