Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17,17,w^{3} - w^{2} - 4w + 2]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} - 3x^{12} - 29x^{11} + 77x^{10} + 298x^{9} - 629x^{8} - 1450x^{7} + 2151x^{6} + 3247x^{5} - 3482x^{4} - 3006x^{3} + 2511x^{2} + 756x - 441\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{13894717}{958972341}e^{12} + \frac{18301189}{319657447}e^{11} - \frac{716165366}{958972341}e^{10} - \frac{1476063085}{958972341}e^{9} + \frac{11554640383}{958972341}e^{8} + \frac{13762438447}{958972341}e^{7} - \frac{71196298252}{958972341}e^{6} - \frac{20529026984}{319657447}e^{5} + \frac{170166919762}{958972341}e^{4} + \frac{102092603413}{958972341}e^{3} - \frac{49245781087}{319657447}e^{2} - \frac{13225422171}{319657447}e + \frac{8316885357}{319657447}$ |
| 7 | $[7, 7, -w^{2} + 2w + 1]$ | $-\frac{197905058}{6712806387}e^{12} + \frac{181259221}{6712806387}e^{11} + \frac{6899271772}{6712806387}e^{10} - \frac{168327162}{319657447}e^{9} - \frac{28958097216}{2237602129}e^{8} + \frac{9001423010}{6712806387}e^{7} + \frac{161109076063}{2237602129}e^{6} + \frac{96186768389}{6712806387}e^{5} - \frac{1118542025243}{6712806387}e^{4} - \frac{288096057106}{6712806387}e^{3} + \frac{956022164002}{6712806387}e^{2} + \frac{40505667870}{2237602129}e - \frac{7451337944}{319657447}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{59403236}{6712806387}e^{12} + \frac{879681091}{6712806387}e^{11} - \frac{5341086244}{6712806387}e^{10} - \frac{3264782713}{958972341}e^{9} + \frac{104736177940}{6712806387}e^{8} + \frac{65548567545}{2237602129}e^{7} - \frac{706366473943}{6712806387}e^{6} - \frac{768546533068}{6712806387}e^{5} + \frac{1816268767274}{6712806387}e^{4} + \frac{377211372814}{2237602129}e^{3} - \frac{1698055968047}{6712806387}e^{2} - \frac{120044518963}{2237602129}e + \frac{14394868831}{319657447}$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{98389359}{2237602129}e^{12} + \frac{203065748}{6712806387}e^{11} - \frac{3970809778}{2237602129}e^{10} - \frac{971081599}{958972341}e^{9} + \frac{167756774329}{6712806387}e^{8} + \frac{87335646119}{6712806387}e^{7} - \frac{981701315953}{6712806387}e^{6} - \frac{527296335053}{6712806387}e^{5} + \frac{769903487859}{2237602129}e^{4} + \frac{1002744280997}{6712806387}e^{3} - \frac{1990183566829}{6712806387}e^{2} - \frac{130846020938}{2237602129}e + \frac{15768223301}{319657447}$ |
| 16 | $[16, 2, 2]$ | $-\frac{231157555}{6712806387}e^{12} - \frac{1472863129}{6712806387}e^{11} + \frac{13961877740}{6712806387}e^{10} + \frac{1847953448}{319657447}e^{9} - \frac{80812669022}{2237602129}e^{8} - \frac{346274937854}{6712806387}e^{7} + \frac{518990844563}{2237602129}e^{6} + \frac{1449879639826}{6712806387}e^{5} - \frac{3880343983615}{6712806387}e^{4} - \frac{2287026790394}{6712806387}e^{3} + \frac{3536792700683}{6712806387}e^{2} + \frac{278858452149}{2237602129}e - \frac{30235263546}{319657447}$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{570339248}{2237602129}e^{12} + \frac{1317718425}{2237602129}e^{11} + \frac{17005714085}{2237602129}e^{10} - \frac{4379342407}{319657447}e^{9} - \frac{179669621710}{2237602129}e^{8} + \frac{197710986372}{2237602129}e^{7} + \frac{867009431956}{2237602129}e^{6} - \frac{360646245217}{2237602129}e^{5} - \frac{1742451619304}{2237602129}e^{4} + \frac{65066235635}{2237602129}e^{3} + \frac{1259025500392}{2237602129}e^{2} + \frac{127196743386}{2237602129}e - \frac{27773177067}{319657447}$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-1$ |
| 25 | $[25, 5, w^{2} - w - 3]$ | $-\frac{2362827802}{6712806387}e^{12} + \frac{5120157368}{6712806387}e^{11} + \frac{71776739663}{6712806387}e^{10} - \frac{5651440023}{319657447}e^{9} - \frac{258923422318}{2237602129}e^{8} + \frac{755599352740}{6712806387}e^{7} + \frac{1277196330797}{2237602129}e^{6} - \frac{1291720604102}{6712806387}e^{5} - \frac{7889307307288}{6712806387}e^{4} + \frac{65200756135}{6712806387}e^{3} + \frac{5878128904169}{6712806387}e^{2} + \frac{166031340801}{2237602129}e - \frac{44274754002}{319657447}$ |
| 37 | $[37, 37, 2w - 1]$ | $-\frac{456233448}{2237602129}e^{12} + \frac{5717165326}{6712806387}e^{11} + \frac{10628664395}{2237602129}e^{10} - \frac{19894345706}{958972341}e^{9} - \frac{216119443507}{6712806387}e^{8} + \frac{1027377797449}{6712806387}e^{7} + \frac{539299092007}{6712806387}e^{6} - \frac{2952658771168}{6712806387}e^{5} - \frac{24857685651}{2237602129}e^{4} + \frac{3197668636027}{6712806387}e^{3} - \frac{942204647351}{6712806387}e^{2} - \frac{238827802271}{2237602129}e + \frac{10829867158}{319657447}$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{534561359}{6712806387}e^{12} + \frac{3053046901}{6712806387}e^{11} + \frac{9716152750}{6712806387}e^{10} - \frac{3619879729}{319657447}e^{9} - \frac{5979384205}{2237602129}e^{8} + \frac{590766310418}{6712806387}e^{7} - \frac{90937219211}{2237602129}e^{6} - \frac{1896869780308}{6712806387}e^{5} + \frac{1287105677329}{6712806387}e^{4} + \frac{2379692289599}{6712806387}e^{3} - \frac{1701879425006}{6712806387}e^{2} - \frac{226269322011}{2237602129}e + \frac{18081415606}{319657447}$ |
| 43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{571714259}{2237602129}e^{12} - \frac{6354971036}{6712806387}e^{11} - \frac{14289638493}{2237602129}e^{10} + \frac{22011635863}{958972341}e^{9} + \frac{339990246665}{6712806387}e^{8} - \frac{1119400922537}{6712806387}e^{7} - \frac{1156409241629}{6712806387}e^{6} + \frac{3064811782511}{6712806387}e^{5} + \frac{433039424520}{2237602129}e^{4} - \frac{3045622727162}{6712806387}e^{3} + \frac{173355543136}{6712806387}e^{2} + \frac{176976828475}{2237602129}e - \frac{8949080204}{319657447}$ |
| 59 | $[59, 59, 2w - 5]$ | $-\frac{2334238693}{6712806387}e^{12} + \frac{2920946283}{2237602129}e^{11} + \frac{58140132641}{6712806387}e^{10} - \frac{30502699130}{958972341}e^{9} - \frac{457897320697}{6712806387}e^{8} + \frac{1569747719642}{6712806387}e^{7} + \frac{1544467362532}{6712806387}e^{6} - \frac{1473665731582}{2237602129}e^{5} - \frac{1759609502746}{6712806387}e^{4} + \frac{4700130457367}{6712806387}e^{3} - \frac{18048683244}{2237602129}e^{2} - \frac{366134964193}{2237602129}e + \frac{6423632376}{319657447}$ |
| 59 | $[59, 59, -2w - 3]$ | $-\frac{155147659}{6712806387}e^{12} + \frac{619482320}{2237602129}e^{11} - \frac{536538952}{6712806387}e^{10} - \frac{6745313279}{958972341}e^{9} + \frac{76129611116}{6712806387}e^{8} + \frac{384009173714}{6712806387}e^{7} - \frac{667813153985}{6712806387}e^{6} - \frac{446892534458}{2237602129}e^{5} + \frac{1957609323455}{6712806387}e^{4} + \frac{1780849735202}{6712806387}e^{3} - \frac{680778111396}{2237602129}e^{2} - \frac{158362273567}{2237602129}e + \frac{18649172898}{319657447}$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $-\frac{830657523}{2237602129}e^{12} + \frac{2883353244}{2237602129}e^{11} + \frac{21383868894}{2237602129}e^{10} - \frac{9919908316}{319657447}e^{9} - \frac{179987787656}{2237602129}e^{8} + \frac{496817133600}{2237602129}e^{7} + \frac{674726551831}{2237602129}e^{6} - \frac{1317439584033}{2237602129}e^{5} - \frac{954752503541}{2237602129}e^{4} + \frac{1268618065136}{2237602129}e^{3} + \frac{263379684255}{2237602129}e^{2} - \frac{228533752749}{2237602129}e + \frac{5821550786}{319657447}$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $-\frac{491893501}{2237602129}e^{12} + \frac{901461823}{2237602129}e^{11} + \frac{15606355724}{2237602129}e^{10} - \frac{2978311440}{319657447}e^{9} - \frac{177424276901}{2237602129}e^{8} + \frac{129711534700}{2237602129}e^{7} + \frac{907346963601}{2237602129}e^{6} - \frac{179708934470}{2237602129}e^{5} - \frac{1933856522303}{2237602129}e^{4} - \frac{105441854053}{2237602129}e^{3} + \frac{1515785291954}{2237602129}e^{2} + \frac{142928417739}{2237602129}e - \frac{37063878655}{319657447}$ |
| 83 | $[83, 83, -w^{3} + 7w]$ | $\phantom{-}\frac{284464864}{958972341}e^{12} - \frac{202278555}{319657447}e^{11} - \frac{8654262743}{958972341}e^{10} + \frac{13940823119}{958972341}e^{9} + \frac{93952388617}{958972341}e^{8} - \frac{86764291190}{958972341}e^{7} - \frac{465710791168}{958972341}e^{6} + \frac{45319306084}{319657447}e^{5} + \frac{961919135920}{958972341}e^{4} + \frac{27028984864}{958972341}e^{3} - \frac{237440326171}{319657447}e^{2} - \frac{26410871078}{319657447}e + \frac{35542657551}{319657447}$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{4458916528}{6712806387}e^{12} - \frac{4623574721}{2237602129}e^{11} - \frac{120554919866}{6712806387}e^{10} + \frac{47351052248}{958972341}e^{9} + \frac{1106519247370}{6712806387}e^{8} - \frac{2319678631610}{6712806387}e^{7} - \frac{4646619238600}{6712806387}e^{6} + \frac{1919728045769}{2237602129}e^{5} + \frac{7932033173320}{6712806387}e^{4} - \frac{4855356532007}{6712806387}e^{3} - \frac{1412183700168}{2237602129}e^{2} + \frac{177737027452}{2237602129}e + \frac{20960659002}{319657447}$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}\frac{930543779}{6712806387}e^{12} - \frac{2924399517}{2237602129}e^{11} - \frac{4424531962}{6712806387}e^{10} + \frac{31380944194}{958972341}e^{9} - \frac{269024780911}{6712806387}e^{8} - \frac{1741195917856}{6712806387}e^{7} + \frac{2618386264966}{6712806387}e^{6} + \frac{1970405080187}{2237602129}e^{5} - \frac{7928656993576}{6712806387}e^{4} - \frac{7860443274367}{6712806387}e^{3} + \frac{2781942558174}{2237602129}e^{2} + \frac{799304331933}{2237602129}e - \frac{72188896458}{319657447}$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}\frac{44950645}{958972341}e^{12} - \frac{13930057}{319657447}e^{11} - \frac{1536226004}{958972341}e^{10} + \frac{709106786}{958972341}e^{9} + \frac{18968238655}{958972341}e^{8} + \frac{451457950}{958972341}e^{7} - \frac{103762053991}{958972341}e^{6} - \frac{13305125204}{319657447}e^{5} + \frac{233267746018}{958972341}e^{4} + \frac{112238064544}{958972341}e^{3} - \frac{63788719888}{319657447}e^{2} - \frac{22266433184}{319657447}e + \frac{9696772377}{319657447}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17,17,w^{3} - w^{2} - 4w + 2]$ | $1$ |