Base field 4.4.13525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29,29,-\frac{1}{5}w^{3} + \frac{12}{5}w - \frac{1}{5}]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} + 3x^{14} - 23x^{13} - 76x^{12} + 149x^{11} + 658x^{10} - 88x^{9} - 2176x^{8} - 1476x^{7} + 2192x^{6} + 2629x^{5} - 210x^{4} - 1182x^{3} - 395x^{2} - 10x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ | $\phantom{-}\frac{95752307}{63244487}e^{14} + \frac{128558854}{63244487}e^{13} - \frac{2422800864}{63244487}e^{12} - \frac{3269218181}{63244487}e^{11} + \frac{19883532072}{63244487}e^{10} + \frac{30255211335}{63244487}e^{9} - \frac{60360404141}{63244487}e^{8} - \frac{110467158749}{63244487}e^{7} + \frac{48386335734}{63244487}e^{6} + \frac{139309969292}{63244487}e^{5} + \frac{11988778965}{63244487}e^{4} - \frac{57190450693}{63244487}e^{3} - \frac{18027790555}{63244487}e^{2} + \frac{1397170238}{63244487}e + \frac{126255219}{63244487}$ |
| 9 | $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ | $-\frac{235568438}{63244487}e^{14} - \frac{370526337}{63244487}e^{13} + \frac{5905730022}{63244487}e^{12} + \frac{9424617584}{63244487}e^{11} - \frac{47518147589}{63244487}e^{10} - \frac{85928531819}{63244487}e^{9} + \frac{135037448065}{63244487}e^{8} + \frac{308433686601}{63244487}e^{7} - \frac{67985026068}{63244487}e^{6} - \frac{379776513005}{63244487}e^{5} - \frac{96006774215}{63244487}e^{4} + \frac{144526782957}{63244487}e^{3} + \frac{71796228431}{63244487}e^{2} + \frac{3556035506}{63244487}e - \frac{413206600}{63244487}$ |
| 9 | $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ | $\phantom{-}\frac{300616356}{63244487}e^{14} + \frac{467502655}{63244487}e^{13} - \frac{7548767757}{63244487}e^{12} - \frac{11880800234}{63244487}e^{11} + \frac{60965200525}{63244487}e^{10} + \frac{108278098048}{63244487}e^{9} - \frac{175423270456}{63244487}e^{8} - \frac{388410589205}{63244487}e^{7} + \frac{99447307949}{63244487}e^{6} + \frac{478426501757}{63244487}e^{5} + \frac{100918780462}{63244487}e^{4} - \frac{186831612768}{63244487}e^{3} - \frac{79916397810}{63244487}e^{2} - \frac{29453745}{63244487}e + \frac{188068850}{63244487}$ |
| 11 | $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ | $-\frac{320438407}{63244487}e^{14} - \frac{542097751}{63244487}e^{13} + \frac{8024140123}{63244487}e^{12} + \frac{13824592917}{63244487}e^{11} - \frac{64399273768}{63244487}e^{10} - \frac{125809045217}{63244487}e^{9} + \frac{180422692588}{63244487}e^{8} + \frac{452907522300}{63244487}e^{7} - \frac{76136649344}{63244487}e^{6} - \frac{568408043070}{63244487}e^{5} - \frac{157753950354}{63244487}e^{4} + \frac{225509240907}{63244487}e^{3} + \frac{110614812304}{63244487}e^{2} + \frac{2490137279}{63244487}e - \frac{219896193}{63244487}$ |
| 11 | $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ | $\phantom{-}\frac{130543335}{63244487}e^{14} + \frac{207463673}{63244487}e^{13} - \frac{3299269461}{63244487}e^{12} - \frac{5294282384}{63244487}e^{11} + \frac{26995224224}{63244487}e^{10} + \frac{48496503914}{63244487}e^{9} - \frac{80059019627}{63244487}e^{8} - \frac{176652929439}{63244487}e^{7} + \frac{52985403250}{63244487}e^{6} + \frac{227561446443}{63244487}e^{5} + \frac{39904335064}{63244487}e^{4} - \frac{95135401993}{63244487}e^{3} - \frac{37162354085}{63244487}e^{2} + \frac{946111559}{63244487}e + \frac{153356551}{63244487}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{165548125}{63244487}e^{14} + \frac{253829572}{63244487}e^{13} - \frac{4125858013}{63244487}e^{12} - \frac{6440609663}{63244487}e^{11} + \frac{32786433696}{63244487}e^{10} + \frac{58608479002}{63244487}e^{9} - \frac{90306766744}{63244487}e^{8} - \frac{208183504735}{63244487}e^{7} + \frac{35189107440}{63244487}e^{6} + \frac{246535811742}{63244487}e^{5} + \frac{76928957701}{63244487}e^{4} - \frac{84759879819}{63244487}e^{3} - \frac{50880704383}{63244487}e^{2} - \frac{6047980991}{63244487}e - \frac{81133254}{63244487}$ |
| 29 | $[29, 29, -w]$ | $-\frac{99538099}{63244487}e^{14} - \frac{234213106}{63244487}e^{13} + \frac{2416212753}{63244487}e^{12} + \frac{5951849654}{63244487}e^{11} - \frac{18092002233}{63244487}e^{10} - \frac{52562297806}{63244487}e^{9} + \frac{38496741963}{63244487}e^{8} + \frac{181286331884}{63244487}e^{7} + \frac{38019677911}{63244487}e^{6} - \frac{210675404836}{63244487}e^{5} - \frac{116698684313}{63244487}e^{4} + \frac{71373709671}{63244487}e^{3} + \frac{55761353235}{63244487}e^{2} + \frac{5716501940}{63244487}e - \frac{70517287}{63244487}$ |
| 29 | $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ | $\phantom{-}\frac{248743091}{63244487}e^{14} + \frac{492034679}{63244487}e^{13} - \frac{6205082849}{63244487}e^{12} - \frac{12613522088}{63244487}e^{11} + \frac{49366920916}{63244487}e^{10} + \frac{114416643041}{63244487}e^{9} - \frac{132219708230}{63244487}e^{8} - \frac{414098839922}{63244487}e^{7} + \frac{21002732591}{63244487}e^{6} + \frac{536123599957}{63244487}e^{5} + \frac{187582109594}{63244487}e^{4} - \frac{221000998128}{63244487}e^{3} - \frac{118250142631}{63244487}e^{2} - \frac{3410156246}{63244487}e - \frac{265711648}{63244487}$ |
| 41 | $[41, 41, -w^{2} + 10]$ | $\phantom{-}\frac{195229694}{63244487}e^{14} + \frac{463567501}{63244487}e^{13} - \frac{4804897745}{63244487}e^{12} - \frac{11901108913}{63244487}e^{11} + \frac{37078884288}{63244487}e^{10} + \frac{106939876020}{63244487}e^{9} - \frac{87277435346}{63244487}e^{8} - \frac{383469764472}{63244487}e^{7} - \frac{48544106332}{63244487}e^{6} + \frac{492847720888}{63244487}e^{5} + \frac{237564549188}{63244487}e^{4} - \frac{196283681935}{63244487}e^{3} - \frac{132722118124}{63244487}e^{2} - \frac{9234599429}{63244487}e + \frac{96820847}{63244487}$ |
| 41 | $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ | $-\frac{62938151}{63244487}e^{14} - \frac{109143675}{63244487}e^{13} + \frac{1584055706}{63244487}e^{12} + \frac{2795969436}{63244487}e^{11} - \frac{12831942074}{63244487}e^{10} - \frac{25582845369}{63244487}e^{9} + \frac{36535301129}{63244487}e^{8} + \frac{93408597673}{63244487}e^{7} - \frac{15738196392}{63244487}e^{6} - \frac{121109746063}{63244487}e^{5} - \frac{37482506616}{63244487}e^{4} + \frac{46944517859}{63244487}e^{3} + \frac{27439548853}{63244487}e^{2} + \frac{3305101107}{63244487}e + \frac{275701630}{63244487}$ |
| 41 | $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ | $\phantom{-}\frac{278989471}{63244487}e^{14} + \frac{530844866}{63244487}e^{13} - \frac{6895059621}{63244487}e^{12} - \frac{13485958701}{63244487}e^{11} + \frac{53786200690}{63244487}e^{10} + \frac{120786039200}{63244487}e^{9} - \frac{136790381810}{63244487}e^{8} - \frac{423633566984}{63244487}e^{7} - \frac{2136697247}{63244487}e^{6} + \frac{502939267133}{63244487}e^{5} + \frac{207336995437}{63244487}e^{4} - \frac{178112912833}{63244487}e^{3} - \frac{116550691686}{63244487}e^{2} - \frac{9738616660}{63244487}e + \frac{210177557}{63244487}$ |
| 49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ | $-\frac{34271918}{63244487}e^{14} - \frac{225509905}{63244487}e^{13} + \frac{747697570}{63244487}e^{12} + \frac{5750677652}{63244487}e^{11} - \frac{4105621936}{63244487}e^{10} - \frac{49093209592}{63244487}e^{9} - \frac{8799943622}{63244487}e^{8} + \frac{164940619423}{63244487}e^{7} + \frac{100235807747}{63244487}e^{6} - \frac{195241708318}{63244487}e^{5} - \frac{148842527083}{63244487}e^{4} + \frac{72827582632}{63244487}e^{3} + \frac{60806262592}{63244487}e^{2} + \frac{1639908850}{63244487}e - \frac{432915228}{63244487}$ |
| 49 | $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ | $-\frac{21306154}{63244487}e^{14} + \frac{92299539}{63244487}e^{13} + \frac{609635954}{63244487}e^{12} - \frac{2373278325}{63244487}e^{11} - \frac{6209942706}{63244487}e^{10} + \frac{19422133195}{63244487}e^{9} + \frac{32061028134}{63244487}e^{8} - \frac{63205975304}{63244487}e^{7} - \frac{85322083251}{63244487}e^{6} + \frac{77592433742}{63244487}e^{5} + \frac{93774243319}{63244487}e^{4} - \frac{31778700226}{63244487}e^{3} - \frac{34563951447}{63244487}e^{2} + \frac{59446270}{63244487}e + \frac{479700609}{63244487}$ |
| 59 | $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ | $\phantom{-}\frac{1325751}{63244487}e^{14} - \frac{113954151}{63244487}e^{13} - \frac{114667334}{63244487}e^{12} + \frac{2921181607}{63244487}e^{11} + \frac{2313616827}{63244487}e^{10} - \frac{24569191507}{63244487}e^{9} - \frac{21140022330}{63244487}e^{8} + \frac{81586093501}{63244487}e^{7} + \frac{78695346752}{63244487}e^{6} - \frac{97780995916}{63244487}e^{5} - \frac{96841502637}{63244487}e^{4} + \frac{38301378147}{63244487}e^{3} + \frac{37262355144}{63244487}e^{2} + \frac{273639702}{63244487}e - \frac{504723149}{63244487}$ |
| 59 | $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ | $-\frac{576522517}{63244487}e^{14} - \frac{995503388}{63244487}e^{13} + \frac{14372164850}{63244487}e^{12} + \frac{25300423182}{63244487}e^{11} - \frac{114301896766}{63244487}e^{10} - \frac{228509755747}{63244487}e^{9} + \frac{312282514569}{63244487}e^{8} + \frac{810736942814}{63244487}e^{7} - \frac{105214140459}{63244487}e^{6} - \frac{983674526581}{63244487}e^{5} - \frac{288498839492}{63244487}e^{4} + \frac{374237761359}{63244487}e^{3} + \frac{183223877697}{63244487}e^{2} + \frac{4258793590}{63244487}e + \frac{156991501}{63244487}$ |
| 61 | $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ | $-\frac{209085339}{63244487}e^{14} - \frac{319773260}{63244487}e^{13} + \frac{5295011600}{63244487}e^{12} + \frac{8194040944}{63244487}e^{11} - \frac{43468587307}{63244487}e^{10} - \frac{75823443793}{63244487}e^{9} + \frac{129887728341}{63244487}e^{8} + \frac{280373335447}{63244487}e^{7} - \frac{86186245746}{63244487}e^{6} - \frac{369510606545}{63244487}e^{5} - \frac{78765192746}{63244487}e^{4} + \frac{150692748432}{63244487}e^{3} + \frac{73591233129}{63244487}e^{2} + \frac{5525152703}{63244487}e - \frac{158544512}{63244487}$ |
| 61 | $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ | $-\frac{177300504}{63244487}e^{14} + \frac{46215168}{63244487}e^{13} + \frac{4695423954}{63244487}e^{12} - \frac{1265843798}{63244487}e^{11} - \frac{42101013988}{63244487}e^{10} + \frac{6174897661}{63244487}e^{9} + \frac{164290641170}{63244487}e^{8} - \frac{5698417141}{63244487}e^{7} - \frac{293215549381}{63244487}e^{6} + \frac{2519924701}{63244487}e^{5} + \frac{240591133427}{63244487}e^{4} + \frac{2487805425}{63244487}e^{3} - \frac{71832226026}{63244487}e^{2} - \frac{6981006323}{63244487}e + \frac{549960303}{63244487}$ |
| 71 | $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ | $-\frac{85885054}{63244487}e^{14} + \frac{89226610}{63244487}e^{13} + \frac{2320183339}{63244487}e^{12} - \frac{2366120920}{63244487}e^{11} - \frac{21541618899}{63244487}e^{10} + \frac{18378514542}{63244487}e^{9} + \frac{91085156128}{63244487}e^{8} - \frac{57889103556}{63244487}e^{7} - \frac{188084766720}{63244487}e^{6} + \frac{77620256075}{63244487}e^{5} + \frac{181495295533}{63244487}e^{4} - \frac{33001109468}{63244487}e^{3} - \frac{63697878314}{63244487}e^{2} - \frac{4196762482}{63244487}e + \frac{430645485}{63244487}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,-\frac{1}{5}w^{3} + \frac{12}{5}w - \frac{1}{5}]$ | $-1$ |