Properties

Label 6.6.1541581.1-37.1-b
Base field 6.6.1541581.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $37$
Level $[37, 37, -w^{2} + 2w + 2]$
Dimension $14$
CM no
Base change no

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Base field 6.6.1541581.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[37, 37, -w^{2} + 2w + 2]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $40$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{14} + 6x^{13} - 28x^{12} - 223x^{11} + 156x^{10} + 2994x^{9} + 1728x^{8} - 17607x^{7} - 20847x^{6} + 43541x^{5} + 67219x^{4} - 38667x^{3} - 76576x^{2} + 2274x + 19820\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ $\phantom{-}e$
11 $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ $-\frac{7629712370361}{10743641442099071}e^{13} - \frac{104235495449421}{21487282884198142}e^{12} + \frac{157771177204832}{10743641442099071}e^{11} + \frac{1839156409222849}{10743641442099071}e^{10} + \frac{673335678250497}{10743641442099071}e^{9} - \frac{45070602853978015}{21487282884198142}e^{8} - \frac{67139817125954951}{21487282884198142}e^{7} + \frac{20064219069051799}{1953389353108922}e^{6} + \frac{462057419205606053}{21487282884198142}e^{5} - \frac{171925628147298948}{10743641442099071}e^{4} - \frac{84564841987745839}{1953389353108922}e^{3} + \frac{38516431069125369}{10743641442099071}e^{2} + \frac{19687785977654626}{976694676554461}e - \frac{10684950218412436}{10743641442099071}$
11 $[11, 11, w^{2} - w - 2]$ $\phantom{-}\frac{502802318308391}{64461848652594426}e^{13} + \frac{1097197024923514}{32230924326297213}e^{12} - \frac{5319964712680131}{21487282884198142}e^{11} - \frac{78148733348272181}{64461848652594426}e^{10} + \frac{77351010875200343}{32230924326297213}e^{9} + \frac{487992837100647041}{32230924326297213}e^{8} - \frac{295372104431529179}{64461848652594426}e^{7} - \frac{227788329262724762}{2930084029663383}e^{6} - \frac{1077916833114975592}{32230924326297213}e^{5} + \frac{4613058689056001797}{32230924326297213}e^{4} + \frac{545672482106124401}{5860168059326766}e^{3} - \frac{2530623533389038100}{32230924326297213}e^{2} - \frac{110026047950322628}{2930084029663383}e + \frac{491603708862929209}{32230924326297213}$
17 $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ $-\frac{18184373419717}{2930084029663383}e^{13} - \frac{184698289701143}{5860168059326766}e^{12} + \frac{171458115272678}{976694676554461}e^{11} + \frac{3215747644208365}{2930084029663383}e^{10} - \frac{3408187395062849}{2930084029663383}e^{9} - \frac{77031985742589379}{5860168059326766}e^{8} - \frac{31165194317028697}{5860168059326766}e^{7} + \frac{359702755510675103}{5860168059326766}e^{6} + \frac{404534835865263101}{5860168059326766}e^{5} - \frac{238039828331046655}{2930084029663383}e^{4} - \frac{788454622105878673}{5860168059326766}e^{3} - \frac{16887676532930300}{2930084029663383}e^{2} + \frac{107387474202253541}{2930084029663383}e + \frac{9834076406744888}{2930084029663383}$
27 $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ $-\frac{45297482925731}{32230924326297213}e^{13} - \frac{1441412019971197}{64461848652594426}e^{12} - \frac{615891926211219}{21487282884198142}e^{11} + \frac{45413039483284531}{64461848652594426}e^{10} + \frac{137471747074321789}{64461848652594426}e^{9} - \frac{216264451878524395}{32230924326297213}e^{8} - \frac{1947327614988768653}{64461848652594426}e^{7} + \frac{33299942735852536}{2930084029663383}e^{6} + \frac{9965455749928779079}{64461848652594426}e^{5} + \frac{6560855512649973113}{64461848652594426}e^{4} - \frac{688335775671452414}{2930084029663383}e^{3} - \frac{8515817051636089684}{32230924326297213}e^{2} + \frac{115451305447844165}{2930084029663383}e + \frac{2690135404062543193}{32230924326297213}$
27 $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ $\phantom{-}\frac{237926366276293}{32230924326297213}e^{13} + \frac{2623380152393399}{64461848652594426}e^{12} - \frac{4419777373586591}{21487282884198142}e^{11} - \frac{92217454470435659}{64461848652594426}e^{10} + \frac{81705657552782353}{64461848652594426}e^{9} + \frac{562643800045579325}{32230924326297213}e^{8} + \frac{507723999383539567}{64461848652594426}e^{7} - \frac{249855373547731973}{2930084029663383}e^{6} - \frac{5879763436951081631}{64461848652594426}e^{5} + \frac{8714151633351554345}{64461848652594426}e^{4} + \frac{535128482566950043}{2930084029663383}e^{3} - \frac{1452723360985593382}{32230924326297213}e^{2} - \frac{183330726087249385}{2930084029663383}e + \frac{569781292215202435}{32230924326297213}$
37 $[37, 37, -w^{2} + 2w + 2]$ $\phantom{-}1$
47 $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ $\phantom{-}\frac{93805342579907}{64461848652594426}e^{13} + \frac{551150675484418}{32230924326297213}e^{12} + \frac{223517003717751}{10743641442099071}e^{11} - \frac{16150496322048292}{32230924326297213}e^{10} - \frac{122050349740438745}{64461848652594426}e^{9} + \frac{246514511455340179}{64461848652594426}e^{8} + \frac{1763938886356898065}{64461848652594426}e^{7} + \frac{40691583655520477}{5860168059326766}e^{6} - \frac{4508687561717127703}{32230924326297213}e^{5} - \frac{9793554613917587035}{64461848652594426}e^{4} + \frac{599819938632749824}{2930084029663383}e^{3} + \frac{10036229073383289269}{32230924326297213}e^{2} - \frac{54485877290213668}{2930084029663383}e - \frac{2838864560752579901}{32230924326297213}$
53 $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ $\phantom{-}\frac{16762402510121}{64461848652594426}e^{13} + \frac{998778890964869}{64461848652594426}e^{12} + \frac{963919844477981}{21487282884198142}e^{11} - \frac{33037393586804741}{64461848652594426}e^{10} - \frac{57413717903931982}{32230924326297213}e^{9} + \frac{354577878304540201}{64461848652594426}e^{8} + \frac{724605243739533608}{32230924326297213}e^{7} - \frac{107023158434462263}{5860168059326766}e^{6} - \frac{7173875794167032453}{64461848652594426}e^{5} - \frac{608649495088985147}{32230924326297213}e^{4} + \frac{515615756998458229}{2930084029663383}e^{3} + \frac{3054402285256649939}{32230924326297213}e^{2} - \frac{135919408893127375}{2930084029663383}e - \frac{918047055686961404}{32230924326297213}$
59 $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ $-\frac{249135934165915}{64461848652594426}e^{13} - \frac{389271102997855}{64461848652594426}e^{12} + \frac{1774620328451673}{10743641442099071}e^{11} + \frac{7994345663712863}{32230924326297213}e^{10} - \frac{173387197388812943}{64461848652594426}e^{9} - \frac{123978158523696241}{32230924326297213}e^{8} + \frac{668160128176430303}{32230924326297213}e^{7} + \frac{82030168578089878}{2930084029663383}e^{6} - \frac{4852122865204223687}{64461848652594426}e^{5} - \frac{6102552598592509165}{64461848652594426}e^{4} + \frac{632077949100613241}{5860168059326766}e^{3} + \frac{3877294954515189344}{32230924326297213}e^{2} - \frac{118858600126015819}{2930084029663383}e - \frac{953569788135289169}{32230924326297213}$
64 $[64, 2, -2]$ $-\frac{190048549281197}{64461848652594426}e^{13} + \frac{337660493453615}{32230924326297213}e^{12} + \frac{4354429194266995}{21487282884198142}e^{11} - \frac{15481421189594491}{64461848652594426}e^{10} - \frac{152184816117121574}{32230924326297213}e^{9} - \frac{262335696240308}{32230924326297213}e^{8} + \frac{3085424544824765879}{64461848652594426}e^{7} + \frac{96834476905141676}{2930084029663383}e^{6} - \frac{6716799674180395259}{32230924326297213}e^{5} - \frac{7555397546385644260}{32230924326297213}e^{4} + \frac{1707695497668439825}{5860168059326766}e^{3} + \frac{13367383794285451405}{32230924326297213}e^{2} - \frac{107988792784801070}{2930084029663383}e - \frac{3754632138375263263}{32230924326297213}$
67 $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ $-\frac{262728237273592}{32230924326297213}e^{13} - \frac{1172980978021823}{64461848652594426}e^{12} + \frac{7394741111234779}{21487282884198142}e^{11} + \frac{48140889853341617}{64461848652594426}e^{10} - \frac{354944159808508723}{64461848652594426}e^{9} - \frac{373526237470838822}{32230924326297213}e^{8} + \frac{2655200340076870727}{64461848652594426}e^{7} + \frac{247867166630431760}{2930084029663383}e^{6} - \frac{9018331562904506263}{64461848652594426}e^{5} - \frac{18599947644685574573}{64461848652594426}e^{4} + \frac{467481994106641343}{2930084029663383}e^{3} + \frac{12131710208335280776}{32230924326297213}e^{2} + \frac{13012171780614019}{2930084029663383}e - \frac{3141776108206789432}{32230924326297213}$
67 $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ $\phantom{-}\frac{343254719781719}{64461848652594426}e^{13} + \frac{501512648493298}{32230924326297213}e^{12} - \frac{4439798532432453}{21487282884198142}e^{11} - \frac{39462588137220401}{64461848652594426}e^{10} + \frac{95122810617361631}{32230924326297213}e^{9} + \frac{289244992726187918}{32230924326297213}e^{8} - \frac{1219481238317383427}{64461848652594426}e^{7} - \frac{178214089822872077}{2930084029663383}e^{6} + \frac{1658776938705192671}{32230924326297213}e^{5} + \frac{6126783970903967836}{32230924326297213}e^{4} - \frac{219025173161516431}{5860168059326766}e^{3} - \frac{7516002734979940540}{32230924326297213}e^{2} - \frac{79093265726316451}{2930084029663383}e + \frac{1909335098033616454}{32230924326297213}$
71 $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}\frac{360805709536445}{32230924326297213}e^{13} + \frac{2982575358090901}{64461848652594426}e^{12} - \frac{3966487292456017}{10743641442099071}e^{11} - \frac{53405075960428163}{32230924326297213}e^{10} + \frac{127325336665442161}{32230924326297213}e^{9} + \frac{1346605101837377669}{64461848652594426}e^{8} - \frac{845456268888273925}{64461848652594426}e^{7} - \frac{640017868609480223}{5860168059326766}e^{6} - \frac{818920846081142353}{64461848652594426}e^{5} + \frac{6753675554024763626}{32230924326297213}e^{4} + \frac{370331151682497541}{5860168059326766}e^{3} - \frac{3886766978789167478}{32230924326297213}e^{2} - \frac{49954265465488220}{2930084029663383}e + \frac{502254005647624514}{32230924326297213}$
71 $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $-\frac{414103853296907}{32230924326297213}e^{13} - \frac{4010451791691307}{64461848652594426}e^{12} + \frac{4068704043467453}{10743641442099071}e^{11} + \frac{70263864720428348}{32230924326297213}e^{10} - \frac{94642890171988897}{32230924326297213}e^{9} - \frac{1704765667306833599}{64461848652594426}e^{8} - \frac{305098504951980293}{64461848652594426}e^{7} + \frac{747800822979950957}{5860168059326766}e^{6} + \frac{7341246543934355695}{64461848652594426}e^{5} - \frac{6284782879798905008}{32230924326297213}e^{4} - \frac{1406863858498781329}{5860168059326766}e^{3} + \frac{1802525934086831192}{32230924326297213}e^{2} + \frac{220644768345667052}{2930084029663383}e - \frac{791399652200635829}{32230924326297213}$
73 $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ $-\frac{199837359405754}{32230924326297213}e^{13} - \frac{1566347384603785}{32230924326297213}e^{12} + \frac{1882635436599543}{21487282884198142}e^{11} + \frac{101576380975042769}{64461848652594426}e^{10} + \frac{122370854631378041}{64461848652594426}e^{9} - \frac{1041981062596851493}{64461848652594426}e^{8} - \frac{1352577211869677972}{32230924326297213}e^{7} + \frac{259622414738657389}{5860168059326766}e^{6} + \frac{7716442639394328166}{32230924326297213}e^{5} + \frac{7914146629221043213}{64461848652594426}e^{4} - \frac{2086158063533546213}{5860168059326766}e^{3} - \frac{13137828280688889077}{32230924326297213}e^{2} + \frac{68129697285062209}{2930084029663383}e + \frac{4028874653147576816}{32230924326297213}$
83 $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ $-\frac{918537056052067}{64461848652594426}e^{13} - \frac{3255289401165217}{64461848652594426}e^{12} + \frac{11361841550744997}{21487282884198142}e^{11} + \frac{123799082796367435}{64461848652594426}e^{10} - \frac{227150125378160185}{32230924326297213}e^{9} - \frac{1726289580762473087}{64461848652594426}e^{8} + \frac{1299299199577646825}{32230924326297213}e^{7} + \frac{987662784809324609}{5860168059326766}e^{6} - \frac{5712539607691707437}{64461848652594426}e^{5} - \frac{15345196291490357021}{32230924326297213}e^{4} + \frac{93909381445174798}{2930084029663383}e^{3} + \frac{17616444899726444432}{32230924326297213}e^{2} + \frac{197894713964038910}{2930084029663383}e - \frac{5313584259889067936}{32230924326297213}$
83 $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ $-\frac{798859803352555}{64461848652594426}e^{13} - \frac{2233980027433463}{32230924326297213}e^{12} + \frac{6980967710847093}{21487282884198142}e^{11} + \frac{153856334071805425}{64461848652594426}e^{10} - \frac{45614266792477765}{32230924326297213}e^{9} - \frac{900469107725702131}{32230924326297213}e^{8} - \frac{1399414810375764011}{64461848652594426}e^{7} + \frac{359769943827857785}{2930084029663383}e^{6} + \frac{6162996204229318376}{32230924326297213}e^{5} - \frac{3809907111060974810}{32230924326297213}e^{4} - \frac{2017523881545093367}{5860168059326766}e^{3} - \frac{3310481249061387622}{32230924326297213}e^{2} + \frac{212532260184727238}{2930084029663383}e + \frac{774104198848154266}{32230924326297213}$
89 $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ $\phantom{-}\frac{534815406315577}{64461848652594426}e^{13} + \frac{1048960681762904}{32230924326297213}e^{12} - \frac{3099219964403919}{10743641442099071}e^{11} - \frac{38895664413235163}{32230924326297213}e^{10} + \frac{220410641516719721}{64461848652594426}e^{9} + \frac{1041408652982097275}{64461848652594426}e^{8} - \frac{975786958077870223}{64461848652594426}e^{7} - \frac{556428605961019511}{5860168059326766}e^{6} + \frac{376652076498843154}{32230924326297213}e^{5} + \frac{15450313069616325037}{64461848652594426}e^{4} + \frac{112485263253449768}{2930084029663383}e^{3} - \frac{8040972728489024117}{32230924326297213}e^{2} - \frac{140916160817447396}{2930084029663383}e + \frac{2421519469332986459}{32230924326297213}$
97 $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ $\phantom{-}\frac{224696119441142}{32230924326297213}e^{13} + \frac{992510060348978}{32230924326297213}e^{12} - \frac{4709095262435881}{21487282884198142}e^{11} - \frac{70400335454976073}{64461848652594426}e^{10} + \frac{132933337401399191}{64461848652594426}e^{9} + \frac{872695866846675257}{64461848652594426}e^{8} - \frac{95853613682183705}{32230924326297213}e^{7} - \frac{401597283234107093}{5860168059326766}e^{6} - \frac{1157159735351023112}{32230924326297213}e^{5} + \frac{7940178089668071529}{64461848652594426}e^{4} + \frac{546827940162435577}{5860168059326766}e^{3} - \frac{2464287098236785068}{32230924326297213}e^{2} - \frac{115443663463850126}{2930084029663383}e + \frac{1078771515733162997}{32230924326297213}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, -w^{2} + 2w + 2]$ $-1$