Base field 4.4.17069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ |
| Dimension: | $15$ |
| 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:
| \(x^{15} + 2x^{14} - 22x^{13} - 46x^{12} + 163x^{11} + 351x^{10} - 519x^{9} - 1159x^{8} + 701x^{7} + 1669x^{6} - 342x^{5} - 914x^{4} + 83x^{3} + 200x^{2} - 8x - 15\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{67533}{95609}e^{14} - \frac{276915}{95609}e^{13} + \frac{1331416}{95609}e^{12} + \frac{6222871}{95609}e^{11} - \frac{7443428}{95609}e^{10} - \frac{46855187}{95609}e^{9} + \frac{9139934}{95609}e^{8} + \frac{151035198}{95609}e^{7} + \frac{30880731}{95609}e^{6} - \frac{203137169}{95609}e^{5} - \frac{72810653}{95609}e^{4} + \frac{87291885}{95609}e^{3} + \frac{31250131}{95609}e^{2} - \frac{10874006}{95609}e - \frac{3715331}{95609}$ |
| 3 | $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $\phantom{-}\frac{254412}{95609}e^{14} + \frac{447967}{95609}e^{13} - \frac{5414595}{95609}e^{12} - \frac{10187825}{95609}e^{11} + \frac{37463916}{95609}e^{10} + \frac{75160847}{95609}e^{9} - \frac{100908342}{95609}e^{8} - \frac{233661519}{95609}e^{7} + \frac{72603760}{95609}e^{6} + \frac{298853621}{95609}e^{5} + \frac{64164356}{95609}e^{4} - \frac{121033905}{95609}e^{3} - \frac{47099431}{95609}e^{2} + \frac{15108952}{95609}e + \frac{6548890}{95609}$ |
| 16 | $[16, 2, 2]$ | $-\frac{409904}{95609}e^{14} - \frac{816755}{95609}e^{13} + \frac{8774270}{95609}e^{12} + \frac{18542682}{95609}e^{11} - \frac{61430667}{95609}e^{10} - \frac{137672768}{95609}e^{9} + \frac{172191024}{95609}e^{8} + \frac{432131360}{95609}e^{7} - \frac{156397634}{95609}e^{6} - \frac{558147991}{95609}e^{5} - \frac{34196182}{95609}e^{4} + \frac{224387889}{95609}e^{3} + \frac{36175773}{95609}e^{2} - \frac{26535533}{95609}e - \frac{5372069}{95609}$ |
| 17 | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $\phantom{-}\frac{234050}{95609}e^{14} + \frac{724200}{95609}e^{13} - \frac{4745951}{95609}e^{12} - \frac{16291234}{95609}e^{11} + \frac{28948894}{95609}e^{10} + \frac{121570923}{95609}e^{9} - \frac{53701559}{95609}e^{8} - \frac{385584932}{95609}e^{7} - \frac{45570313}{95609}e^{6} + \frac{504331359}{95609}e^{5} + \frac{185214306}{95609}e^{4} - \frac{204321075}{95609}e^{3} - \frac{84607322}{95609}e^{2} + \frac{24858980}{95609}e + \frac{10128874}{95609}$ |
| 17 | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{146432}{95609}e^{14} + \frac{217388}{95609}e^{13} - \frac{3042725}{95609}e^{12} - \frac{4905922}{95609}e^{11} + \frac{19969243}{95609}e^{10} + \frac{35024484}{95609}e^{9} - \frac{45669294}{95609}e^{8} - \frac{102561916}{95609}e^{7} - \frac{327987}{95609}e^{6} + \frac{116406031}{95609}e^{5} + \frac{95640935}{95609}e^{4} - \frac{33450055}{95609}e^{3} - \frac{50064655}{95609}e^{2} + \frac{2855672}{95609}e + \frac{6111272}{95609}$ |
| 17 | $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ | $-\frac{608830}{95609}e^{14} - \frac{1611237}{95609}e^{13} + \frac{12594752}{95609}e^{12} + \frac{36316598}{95609}e^{11} - \frac{81138185}{95609}e^{10} - \frac{270123249}{95609}e^{9} + \frac{182242168}{95609}e^{8} + \frac{851505352}{95609}e^{7} - \frac{10190732}{95609}e^{6} - \frac{1102694575}{95609}e^{5} - \frac{322609262}{95609}e^{4} + \frac{437217412}{95609}e^{3} + \frac{156279848}{95609}e^{2} - \frac{51252664}{95609}e - \frac{19353247}{95609}$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ | $\phantom{-}\frac{453552}{95609}e^{14} + \frac{480731}{95609}e^{13} - \frac{10031496}{95609}e^{12} - \frac{11159353}{95609}e^{11} + \frac{75519915}{95609}e^{10} + \frac{81727017}{95609}e^{9} - \frac{243836811}{95609}e^{8} - \frac{250336725}{95609}e^{7} + \frac{324819005}{95609}e^{6} + \frac{317829412}{95609}e^{5} - \frac{128955654}{95609}e^{4} - \frac{136329016}{95609}e^{3} + \frac{10474224}{95609}e^{2} + \frac{17936161}{95609}e + \frac{1332131}{95609}$ |
| 25 | $[25, 5, w^{2} - 2w - 7]$ | $\phantom{-}\frac{31315}{95609}e^{14} + \frac{70159}{95609}e^{13} - \frac{775438}{95609}e^{12} - \frac{1616186}{95609}e^{11} + \frac{7055559}{95609}e^{10} + \frac{12535524}{95609}e^{9} - \frac{31736514}{95609}e^{8} - \frac{41686711}{95609}e^{7} + \frac{76070153}{95609}e^{6} + \frac{57367384}{95609}e^{5} - \frac{92500742}{95609}e^{4} - \frac{23140687}{95609}e^{3} + \frac{45126231}{95609}e^{2} + \frac{1828932}{95609}e - \frac{6049413}{95609}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{342235}{95609}e^{14} - \frac{429717}{95609}e^{13} + \frac{7370980}{95609}e^{12} + \frac{9811964}{95609}e^{11} - \frac{52512008}{95609}e^{10} - \frac{70718883}{95609}e^{9} + \frac{150531355}{95609}e^{8} + \frac{210271788}{95609}e^{7} - \frac{138737739}{95609}e^{6} - \frac{247649756}{95609}e^{5} - \frac{41691580}{95609}e^{4} + \frac{82313318}{95609}e^{3} + \frac{47150644}{95609}e^{2} - \frac{8426313}{95609}e - \frac{7141434}{95609}$ |
| 29 | $[29, 29, w - 2]$ | $-\frac{59598}{95609}e^{14} + \frac{391349}{95609}e^{13} + \frac{1708839}{95609}e^{12} - \frac{8596491}{95609}e^{11} - \frac{19032692}{95609}e^{10} + \frac{65265308}{95609}e^{9} + \frac{97380449}{95609}e^{8} - \frac{213358709}{95609}e^{7} - \frac{234841815}{95609}e^{6} + \frac{286951923}{95609}e^{5} + \frac{243226454}{95609}e^{4} - \frac{112862403}{95609}e^{3} - \frac{84344252}{95609}e^{2} + \frac{12307920}{95609}e + \frac{9131152}{95609}$ |
| 53 | $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ | $-\frac{698301}{95609}e^{14} - \frac{1144592}{95609}e^{13} + \frac{15062141}{95609}e^{12} + \frac{26095425}{95609}e^{11} - \frac{107409344}{95609}e^{10} - \frac{192505717}{95609}e^{9} + \frac{311868161}{95609}e^{8} + \frac{597325758}{95609}e^{7} - \frac{314031539}{95609}e^{6} - \frac{759450802}{95609}e^{5} - \frac{14416693}{95609}e^{4} + \frac{299863552}{95609}e^{3} + \frac{49978061}{95609}e^{2} - \frac{34087096}{95609}e - \frac{7537010}{95609}$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ | $\phantom{-}\frac{163058}{95609}e^{14} + \frac{414176}{95609}e^{13} - \frac{3367925}{95609}e^{12} - \frac{9294071}{95609}e^{11} + \frac{21646914}{95609}e^{10} + \frac{68354360}{95609}e^{9} - \frac{48303371}{95609}e^{8} - \frac{210576572}{95609}e^{7} + \frac{1846550}{95609}e^{6} + \frac{257928781}{95609}e^{5} + \frac{84626210}{95609}e^{4} - \frac{82796235}{95609}e^{3} - \frac{36555006}{95609}e^{2} + \frac{6275844}{95609}e + \frac{3818487}{95609}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ | $\phantom{-}\frac{1021595}{95609}e^{14} + \frac{2102019}{95609}e^{13} - \frac{21884154}{95609}e^{12} - \frac{47740428}{95609}e^{11} + \frac{153387963}{95609}e^{10} + \frac{355553191}{95609}e^{9} - \frac{431716944}{95609}e^{8} - \frac{1122453868}{95609}e^{7} + \frac{400210227}{95609}e^{6} + \frac{1465948095}{95609}e^{5} + \frac{69278144}{95609}e^{4} - \frac{605525678}{95609}e^{3} - \frac{85569456}{95609}e^{2} + \frac{72380849}{95609}e + \frac{13007709}{95609}$ |
| 61 | $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ | $\phantom{-}\frac{623221}{95609}e^{14} + \frac{1331888}{95609}e^{13} - \frac{13042163}{95609}e^{12} - \frac{30089627}{95609}e^{11} + \frac{86673483}{95609}e^{10} + \frac{222034738}{95609}e^{9} - \frac{211136319}{95609}e^{8} - \frac{690208315}{95609}e^{7} + \frac{74821834}{95609}e^{6} + \frac{874759048}{95609}e^{5} + \frac{269334107}{95609}e^{4} - \frac{334720128}{95609}e^{3} - \frac{144728135}{95609}e^{2} + \frac{39800228}{95609}e + \frac{17879310}{95609}$ |
| 101 | $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ | $\phantom{-}\frac{35536}{95609}e^{14} - \frac{1544809}{95609}e^{13} - \frac{2200528}{95609}e^{12} + \frac{34156454}{95609}e^{11} + \frac{38841565}{95609}e^{10} - \frac{258061396}{95609}e^{9} - \frac{255825250}{95609}e^{8} + \frac{837069410}{95609}e^{7} + \frac{724252005}{95609}e^{6} - \frac{1120274799}{95609}e^{5} - \frac{834976183}{95609}e^{4} + \frac{450571758}{95609}e^{3} + \frac{297856797}{95609}e^{2} - \frac{53892623}{95609}e - \frac{31788937}{95609}$ |
| 103 | $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{1340870}{95609}e^{14} + \frac{2825972}{95609}e^{13} - \frac{28341109}{95609}e^{12} - \frac{64004378}{95609}e^{11} + \frac{192724918}{95609}e^{10} + \frac{474483663}{95609}e^{9} - \frac{501078571}{95609}e^{8} - \frac{1486893741}{95609}e^{7} + \frac{309924481}{95609}e^{6} + \frac{1915863594}{95609}e^{5} + \frac{388436211}{95609}e^{4} - \frac{766672289}{95609}e^{3} - \frac{245308705}{95609}e^{2} + \frac{89775636}{95609}e + \frac{33557591}{95609}$ |
| 103 | $[103, 103, -w^{3} + w^{2} + 8w + 2]$ | $\phantom{-}\frac{446295}{95609}e^{14} + \frac{1169921}{95609}e^{13} - \frac{9330285}{95609}e^{12} - \frac{26444244}{95609}e^{11} + \frac{61628978}{95609}e^{10} + \frac{197737721}{95609}e^{9} - \frac{149422118}{95609}e^{8} - \frac{628908219}{95609}e^{7} + \frac{56447287}{95609}e^{6} + \frac{828793543}{95609}e^{5} + \frac{177259481}{95609}e^{4} - \frac{344257130}{95609}e^{3} - \frac{98839161}{95609}e^{2} + \frac{41073752}{95609}e + \frac{13317219}{95609}$ |
| 113 | $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}\frac{1630148}{95609}e^{14} + \frac{3836950}{95609}e^{13} - \frac{34086463}{95609}e^{12} - \frac{86718066}{95609}e^{11} + \frac{225730778}{95609}e^{10} + \frac{644373423}{95609}e^{9} - \frac{547478950}{95609}e^{8} - \frac{2028313242}{95609}e^{7} + \frac{194589852}{95609}e^{6} + \frac{2630109216}{95609}e^{5} + \frac{685925180}{95609}e^{4} - \frac{1061606663}{95609}e^{3} - \frac{372139755}{95609}e^{2} + \frac{126347133}{95609}e + \frac{48863599}{95609}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $-1$ |