Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $27$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 3x^{13} - 27x^{12} + 80x^{11} + 274x^{10} - 781x^{9} - 1378x^{8} + 3558x^{7} + 3692x^{6} - 7584x^{5} - 5070x^{4} + 6046x^{3} + 2807x^{2} - 332x - 152\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-\frac{338713}{1563066}e^{13} + \frac{361651}{1563066}e^{12} + \frac{9467465}{1563066}e^{11} - \frac{3985109}{781533}e^{10} - \frac{16480532}{260511}e^{9} + \frac{54797287}{1563066}e^{8} + \frac{81580142}{260511}e^{7} - \frac{20470291}{260511}e^{6} - \frac{569318224}{781533}e^{5} - \frac{10555019}{781533}e^{4} + \frac{484679894}{781533}e^{3} + \frac{85217987}{781533}e^{2} - \frac{20803715}{521022}e - \frac{1517354}{781533}$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $-\frac{63704}{781533}e^{13} - \frac{55378}{781533}e^{12} + \frac{2140621}{781533}e^{11} + \frac{1250116}{781533}e^{10} - \frac{8873197}{260511}e^{9} - \frac{10064680}{781533}e^{8} + \frac{50214470}{260511}e^{7} + \frac{13488794}{260511}e^{6} - \frac{385511851}{781533}e^{5} - \frac{84171758}{781533}e^{4} + \frac{354992666}{781533}e^{3} + \frac{61258379}{781533}e^{2} - \frac{10849088}{260511}e - \frac{2021246}{781533}$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}\frac{456040}{781533}e^{13} - \frac{357256}{781533}e^{12} - \frac{12919538}{781533}e^{11} + \frac{7289260}{781533}e^{10} + \frac{45666820}{260511}e^{9} - \frac{40118641}{781533}e^{8} - \frac{229024372}{260511}e^{7} + \frac{3219893}{260511}e^{6} + \frac{1611113351}{781533}e^{5} + \frac{372498034}{781533}e^{4} - \frac{1368653278}{781533}e^{3} - \frac{523766002}{781533}e^{2} + \frac{26273936}{260511}e + \frac{29739178}{781533}$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{60748}{260511}e^{13} - \frac{23996}{260511}e^{12} - \frac{1788496}{260511}e^{11} + \frac{432757}{260511}e^{10} + \frac{19726693}{260511}e^{9} - \frac{361036}{86837}e^{8} - \frac{33989304}{86837}e^{7} - \frac{4817426}{86837}e^{6} + \frac{243396329}{260511}e^{5} + \frac{78204878}{260511}e^{4} - \frac{206445815}{260511}e^{3} - \frac{90701935}{260511}e^{2} + \frac{8251052}{260511}e + \frac{2056570}{86837}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{37994}{781533}e^{13} - \frac{10831}{781533}e^{12} + \frac{1153795}{781533}e^{11} + \frac{455731}{781533}e^{10} - \frac{4400428}{260511}e^{9} - \frac{6787102}{781533}e^{8} + \frac{23578526}{260511}e^{7} + \frac{14679341}{260511}e^{6} - \frac{172483891}{781533}e^{5} - \frac{123826250}{781533}e^{4} + \frac{139502186}{781533}e^{3} + \frac{114787193}{781533}e^{2} + \frac{4265161}{260511}e - \frac{4848320}{781533}$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{404800}{781533}e^{13} - \frac{447862}{781533}e^{12} - \frac{11150990}{781533}e^{11} + \frac{9583174}{781533}e^{10} + \frac{12737504}{86837}e^{9} - \frac{61854418}{781533}e^{8} - \frac{186753061}{260511}e^{7} + \frac{37322018}{260511}e^{6} + \frac{1292290199}{781533}e^{5} + \frac{135855718}{781533}e^{4} - \frac{1095883081}{781533}e^{3} - \frac{327993163}{781533}e^{2} + \frac{8191066}{86837}e + \frac{22825840}{781533}$ |
| 32 | $[32, 2, 2]$ | $-\frac{51671}{86837}e^{13} + \frac{121126}{260511}e^{12} + \frac{1472336}{86837}e^{11} - \frac{2508025}{260511}e^{10} - \frac{15721999}{86837}e^{9} + \frac{14398045}{260511}e^{8} + \frac{79413098}{86837}e^{7} - \frac{2941468}{86837}e^{6} - \frac{187442035}{86837}e^{5} - \frac{111174160}{260511}e^{4} + \frac{159892698}{86837}e^{3} + \frac{163779523}{260511}e^{2} - \frac{8506892}{86837}e - \frac{9250783}{260511}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{266758}{781533}e^{13} + \frac{538762}{781533}e^{12} + \frac{6672485}{781533}e^{11} - \frac{11869471}{781533}e^{10} - \frac{20169419}{260511}e^{9} + \frac{83929636}{781533}e^{8} + \frac{86580202}{260511}e^{7} - \frac{73980869}{260511}e^{6} - \frac{533734415}{781533}e^{5} + \frac{135649451}{781533}e^{4} + \frac{410522548}{781533}e^{3} + \frac{99785725}{781533}e^{2} - \frac{6719923}{260511}e - \frac{10096654}{781533}$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $-\frac{128701}{1563066}e^{13} - \frac{151997}{1563066}e^{12} + \frac{4174139}{1563066}e^{11} + \frac{1982545}{781533}e^{10} - \frac{8374937}{260511}e^{9} - \frac{38910305}{1563066}e^{8} + \frac{46008959}{260511}e^{7} + \frac{31159424}{260511}e^{6} - \frac{341229877}{781533}e^{5} - \frac{215593721}{781533}e^{4} + \frac{294179249}{781533}e^{3} + \frac{175561817}{781533}e^{2} - \frac{9559031}{521022}e - \frac{6479978}{781533}$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{14129}{86837}e^{13} + \frac{60805}{260511}e^{12} + \frac{1163450}{260511}e^{11} - \frac{1424075}{260511}e^{10} - \frac{11913037}{260511}e^{9} + \frac{3752536}{86837}e^{8} + \frac{19369619}{86837}e^{7} - \frac{12384775}{86837}e^{6} - \frac{44943502}{86837}e^{5} + \frac{47865578}{260511}e^{4} + \frac{118431076}{260511}e^{3} - \frac{18989056}{260511}e^{2} - \frac{12462272}{260511}e + \frac{133978}{86837}$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-\frac{344563}{1563066}e^{13} + \frac{931813}{1563066}e^{12} + \frac{7796993}{1563066}e^{11} - \frac{10233479}{781533}e^{10} - \frac{9929303}{260511}e^{9} + \frac{145026697}{1563066}e^{8} + \frac{32718032}{260511}e^{7} - \frac{65923861}{260511}e^{6} - \frac{132936700}{781533}e^{5} + \frac{154406281}{781533}e^{4} + \frac{35435642}{781533}e^{3} + \frac{37146281}{781533}e^{2} + \frac{19234591}{521022}e - \frac{2708630}{781533}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{513685}{1563066}e^{13} - \frac{580963}{1563066}e^{12} - \frac{14257877}{1563066}e^{11} + \frac{6359660}{781533}e^{10} + \frac{8220050}{86837}e^{9} - \frac{86752831}{1563066}e^{8} - \frac{121731068}{260511}e^{7} + \frac{32233948}{260511}e^{6} + \frac{851643322}{781533}e^{5} + \frac{18144476}{781533}e^{4} - \frac{736632761}{781533}e^{3} - \frac{147167948}{781533}e^{2} + \frac{13904043}{173674}e + \frac{12929408}{781533}$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-\frac{206078}{781533}e^{13} - \frac{57787}{781533}e^{12} + \frac{6362443}{781533}e^{11} + \frac{1918729}{781533}e^{10} - \frac{24539054}{260511}e^{9} - \frac{25273456}{781533}e^{8} + \frac{131924357}{260511}e^{7} + \frac{53322683}{260511}e^{6} - \frac{971410057}{781533}e^{5} - \frac{455874110}{781533}e^{4} + \frac{833779631}{781533}e^{3} + \frac{423425873}{781533}e^{2} - \frac{6304240}{260511}e - \frac{23794622}{781533}$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}\frac{262361}{781533}e^{13} - \frac{102377}{781533}e^{12} - \frac{7694527}{781533}e^{11} + \frac{1805528}{781533}e^{10} + \frac{28255595}{260511}e^{9} - \frac{4333283}{781533}e^{8} - \frac{146652932}{260511}e^{7} - \frac{19056470}{260511}e^{6} + \frac{1061909029}{781533}e^{5} + \frac{301229918}{781533}e^{4} - \frac{930331493}{781533}e^{3} - \frac{341416121}{781533}e^{2} + \frac{22830154}{260511}e + \frac{19991192}{781533}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $-\frac{157817}{781533}e^{13} + \frac{422558}{781533}e^{12} + \frac{3768088}{781533}e^{11} - \frac{9648617}{781533}e^{10} - \frac{10633538}{260511}e^{9} + \frac{73927736}{781533}e^{8} + \frac{42241481}{260511}e^{7} - \frac{79458913}{260511}e^{6} - \frac{246186919}{781533}e^{5} + \frac{308320204}{781533}e^{4} + \frac{198591623}{781533}e^{3} - \frac{126423847}{781533}e^{2} - \frac{9902218}{260511}e + \frac{6590668}{781533}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $\phantom{-}\frac{152707}{781533}e^{13} - \frac{466471}{781533}e^{12} - \frac{3618764}{781533}e^{11} + \frac{11108047}{781533}e^{10} + \frac{10029178}{260511}e^{9} - \frac{91668025}{781533}e^{8} - \frac{38464711}{260511}e^{7} + \frac{111705707}{260511}e^{6} + \frac{215211683}{781533}e^{5} - \frac{544925246}{781533}e^{4} - \frac{178328617}{781533}e^{3} + \frac{333300248}{781533}e^{2} + \frac{13847876}{260511}e - \frac{23068076}{781533}$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}\frac{119089}{781533}e^{13} + \frac{24329}{781533}e^{12} - \frac{3537821}{781533}e^{11} - \frac{1344779}{781533}e^{10} + \frac{13187404}{260511}e^{9} + \frac{22849859}{781533}e^{8} - \frac{69322852}{260511}e^{7} - \frac{52886782}{260511}e^{6} + \frac{501519191}{781533}e^{5} + \frac{462253267}{781533}e^{4} - \frac{412743172}{781533}e^{3} - \frac{436549957}{781533}e^{2} - \frac{1817509}{260511}e + \frac{25387696}{781533}$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{1035149}{1563066}e^{13} + \frac{1070963}{1563066}e^{12} + \frac{28643863}{1563066}e^{11} - \frac{11214133}{781533}e^{10} - \frac{49362950}{260511}e^{9} + \frac{136676051}{1563066}e^{8} + \frac{242644570}{260511}e^{7} - \frac{30382739}{260511}e^{6} - \frac{1684614311}{781533}e^{5} - \frac{291750757}{781533}e^{4} + \frac{1422474808}{781533}e^{3} + \frac{518621917}{781533}e^{2} - \frac{60954335}{521022}e - \frac{35861020}{781533}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-1$ |