Properties

Label 6.6.1241125.1-49.1-a
Base field 6.6.1241125.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$
Dimension $15$
CM no
Base change no

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Base field 6.6.1241125.1

Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$
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:

\(x^{15} + 7x^{14} - 22x^{13} - 237x^{12} + 9x^{11} + 2807x^{10} + 2194x^{9} - 15492x^{8} - 15198x^{7} + 45065x^{6} + 38286x^{5} - 72076x^{4} - 36653x^{3} + 56862x^{2} + 7630x - 13354\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ $\phantom{-}e$
9 $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ $\phantom{-}\frac{1504363229540792067}{146160698785720231801}e^{14} + \frac{11760786763522312777}{146160698785720231801}e^{13} - \frac{23208336507342952576}{146160698785720231801}e^{12} - \frac{373458701580536154521}{146160698785720231801}e^{11} - \frac{297323830557380770642}{146160698785720231801}e^{10} + \frac{3912025430771508715355}{146160698785720231801}e^{9} + \frac{6493839506203570904652}{146160698785720231801}e^{8} - \frac{17240286741835736767803}{146160698785720231801}e^{7} - \frac{36427028596378027798851}{146160698785720231801}e^{6} + \frac{34307569429378539535789}{146160698785720231801}e^{5} + \frac{82996918369984897152272}{146160698785720231801}e^{4} - \frac{32130081221752538733025}{146160698785720231801}e^{3} - \frac{77695884679714210476650}{146160698785720231801}e^{2} + \frac{13653494734526964614402}{146160698785720231801}e + \frac{21626703098563862878576}{146160698785720231801}$
11 $[11, 11, w - 1]$ $-\frac{481402907265757658}{146160698785720231801}e^{14} - \frac{3917794344914564981}{146160698785720231801}e^{13} + \frac{6654685380014286643}{146160698785720231801}e^{12} + \frac{123980137464721654216}{146160698785720231801}e^{11} + \frac{120846929671884645685}{146160698785720231801}e^{10} - \frac{1289560328884793589121}{146160698785720231801}e^{9} - \frac{2368199449061829170770}{146160698785720231801}e^{8} + \frac{5599783751094904074232}{146160698785720231801}e^{7} + \frac{13057061024127687657139}{146160698785720231801}e^{6} - \frac{10810058939091681536959}{146160698785720231801}e^{5} - \frac{29395517822671857503347}{146160698785720231801}e^{4} + \frac{9632017356518942414473}{146160698785720231801}e^{3} + \frac{26534902530157807572758}{146160698785720231801}e^{2} - \frac{4078009106494034368856}{146160698785720231801}e - \frac{6879847594187901980502}{146160698785720231801}$
25 $[25, 5, w^{3} + w^{2} - 4w - 3]$ $-\frac{2862270168039425134}{146160698785720231801}e^{14} - \frac{22548037740141301670}{146160698785720231801}e^{13} + \frac{43435825802176883659}{146160698785720231801}e^{12} + \frac{718493423291352470464}{146160698785720231801}e^{11} + \frac{599151168627617312779}{146160698785720231801}e^{10} - \frac{7577283347570988461101}{146160698785720231801}e^{9} - \frac{12921226149810575123741}{146160698785720231801}e^{8} + \frac{33823699139456063201808}{146160698785720231801}e^{7} + \frac{73579177120341421501624}{146160698785720231801}e^{6} - \frac{68903087070066397125477}{146160698785720231801}e^{5} - \frac{172357049136259300050399}{146160698785720231801}e^{4} + \frac{66913841799985030558436}{146160698785720231801}e^{3} + \frac{167429982748129757136606}{146160698785720231801}e^{2} - \frac{29448694558840429505570}{146160698785720231801}e - \frac{48922313490213699060662}{146160698785720231801}$
29 $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ $\phantom{-}\frac{3371352195470066360}{146160698785720231801}e^{14} + \frac{26170699159654000246}{146160698785720231801}e^{13} - \frac{53596193347548311064}{146160698785720231801}e^{12} - \frac{836694985295869033380}{146160698785720231801}e^{11} - \frac{625468913696283651477}{146160698785720231801}e^{10} + \frac{8880169585145710809145}{146160698785720231801}e^{9} + \frac{14318668208223482884202}{146160698785720231801}e^{8} - \frac{40097464647824247056344}{146160698785720231801}e^{7} - \frac{82190581114183316386379}{146160698785720231801}e^{6} + \frac{83099849456624619253853}{146160698785720231801}e^{5} + \frac{192289581308063835647636}{146160698785720231801}e^{4} - \frac{81569929349421381736497}{146160698785720231801}e^{3} - \frac{184948057751710587379952}{146160698785720231801}e^{2} + \frac{35371376510506330356759}{146160698785720231801}e + \frac{52968987942433797496658}{146160698785720231801}$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-\frac{1552406045668750059}{146160698785720231801}e^{14} - \frac{12386254658102930354}{146160698785720231801}e^{13} + \frac{21996581194760146160}{146160698785720231801}e^{12} + \frac{389969300929715247194}{146160698785720231801}e^{11} + \frac{370595692713837016089}{146160698785720231801}e^{10} - \frac{4014799679343772779007}{146160698785720231801}e^{9} - \frac{7407378361763562188298}{146160698785720231801}e^{8} + \frac{17083895799027667686169}{146160698785720231801}e^{7} + \frac{41044849631714407642019}{146160698785720231801}e^{6} - \frac{31749540694581113731707}{146160698785720231801}e^{5} - \frac{93772119953494975734947}{146160698785720231801}e^{4} + \frac{26965998372103548648502}{146160698785720231801}e^{3} + \frac{88856748219979758559365}{146160698785720231801}e^{2} - \frac{11960226593228313926766}{146160698785720231801}e - \frac{24971780415614304869778}{146160698785720231801}$
49 $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $\phantom{-}1$
59 $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ $-\frac{3621359265104992739}{146160698785720231801}e^{14} - \frac{28082224501900602039}{146160698785720231801}e^{13} + \frac{57804779515516703458}{146160698785720231801}e^{12} + \frac{897644789893569764233}{146160698785720231801}e^{11} + \frac{661047707874647730754}{146160698785720231801}e^{10} - \frac{9527079781494594502591}{146160698785720231801}e^{9} - \frac{15197009309913117668916}{146160698785720231801}e^{8} + \frac{43077218160411992411915}{146160698785720231801}e^{7} + \frac{86879147416184019133963}{146160698785720231801}e^{6} - \frac{89922346878279806547744}{146160698785720231801}e^{5} - \frac{201733730847500801440269}{146160698785720231801}e^{4} + \frac{90390278368614928323017}{146160698785720231801}e^{3} + \frac{192385519682009018779902}{146160698785720231801}e^{2} - \frac{40418887584645958180304}{146160698785720231801}e - \frac{54558876689256037015962}{146160698785720231801}$
59 $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ $\phantom{-}\frac{899561993049662133}{146160698785720231801}e^{14} + \frac{6671658673287553874}{146160698785720231801}e^{13} - \frac{17244836305366585745}{146160698785720231801}e^{12} - \frac{221960041147181592759}{146160698785720231801}e^{11} - \frac{81523991990960951467}{146160698785720231801}e^{10} + \frac{2530481714332283347059}{146160698785720231801}e^{9} + \frac{3085077056628717416199}{146160698785720231801}e^{8} - \frac{12842379589369769414407}{146160698785720231801}e^{7} - \frac{19903999899638410357208}{146160698785720231801}e^{6} + \frac{31262004936005495482994}{146160698785720231801}e^{5} + \frac{50954094189389938910720}{146160698785720231801}e^{4} - \frac{35540281176007651679562}{146160698785720231801}e^{3} - \frac{53016426523932692643482}{146160698785720231801}e^{2} + \frac{15332520422569946086272}{146160698785720231801}e + \frac{17047742108539907264968}{146160698785720231801}$
61 $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ $\phantom{-}\frac{232178559727782031}{146160698785720231801}e^{14} + \frac{2774156625876869530}{146160698785720231801}e^{13} + \frac{2407510773131576260}{146160698785720231801}e^{12} - \frac{80818221447577754325}{146160698785720231801}e^{11} - \frac{241544710835711588705}{146160698785720231801}e^{10} + \frac{697632364092968268631}{146160698785720231801}e^{9} + \frac{3160484001021050434211}{146160698785720231801}e^{8} - \frac{1837720854719275035372}{146160698785720231801}e^{7} - \frac{15981662084846418399815}{146160698785720231801}e^{6} - \frac{477164823266649198883}{146160698785720231801}e^{5} + \frac{35806766081125518487355}{146160698785720231801}e^{4} + \frac{4241352489780565556606}{146160698785720231801}e^{3} - \frac{34028962779393691968098}{146160698785720231801}e^{2} - \frac{4585516294733194516}{146160698785720231801}e + \frac{9440452829786915311550}{146160698785720231801}$
61 $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ $-\frac{351682979259545449}{146160698785720231801}e^{14} - \frac{2643405753271749789}{146160698785720231801}e^{13} + \frac{5870921871762744932}{146160698785720231801}e^{12} + \frac{83105749849979847883}{146160698785720231801}e^{11} + \frac{50007632213764088257}{146160698785720231801}e^{10} - \frac{859720577625508749271}{146160698785720231801}e^{9} - \frac{1205824828059061533791}{146160698785720231801}e^{8} + \frac{3803815235283567566932}{146160698785720231801}e^{7} + \frac{6265979841444416744709}{146160698785720231801}e^{6} - \frac{8367066834649922491600}{146160698785720231801}e^{5} - \frac{12090852585198390554967}{146160698785720231801}e^{4} + \frac{10795124724995881849479}{146160698785720231801}e^{3} + \frac{8648675500776062480906}{146160698785720231801}e^{2} - \frac{6364273812697708463774}{146160698785720231801}e - \frac{1816905059674402703936}{146160698785720231801}$
64 $[64, 2, 2]$ $\phantom{-}\frac{2685392287129037130}{146160698785720231801}e^{14} + \frac{20711126789450370775}{146160698785720231801}e^{13} - \frac{42547390543012304709}{146160698785720231801}e^{12} - \frac{659573539627520427004}{146160698785720231801}e^{11} - \frac{503378095184801041522}{146160698785720231801}e^{10} + \frac{6940516747909036851089}{146160698785720231801}e^{9} + \frac{11471515169222881679141}{146160698785720231801}e^{8} - \frac{30737184627283787358651}{146160698785720231801}e^{7} - \frac{65835470216236465889283}{146160698785720231801}e^{6} + \frac{61046308832486071179268}{146160698785720231801}e^{5} + \frac{153924495835719795956657}{146160698785720231801}e^{4} - \frac{55921493723331624494151}{146160698785720231801}e^{3} - \frac{147386369895101478595776}{146160698785720231801}e^{2} + \frac{23792322356790740990772}{146160698785720231801}e + \frac{41192579702639320431199}{146160698785720231801}$
71 $[71, 71, w^{3} + w^{2} - 5w - 3]$ $\phantom{-}\frac{3073051728510043733}{146160698785720231801}e^{14} + \frac{24656889412727588210}{146160698785720231801}e^{13} - \frac{44622061082888699305}{146160698785720231801}e^{12} - \frac{785877871676160530812}{146160698785720231801}e^{11} - \frac{711327921174717327250}{146160698785720231801}e^{10} + \frac{8297132953126575260043}{146160698785720231801}e^{9} + \frac{14670339310930347886934}{146160698785720231801}e^{8} - \frac{37197903098105405886534}{146160698785720231801}e^{7} - \frac{83213952487319090971564}{146160698785720231801}e^{6} + \frac{76865457255407779757624}{146160698785720231801}e^{5} + \frac{195715190961054360925682}{146160698785720231801}e^{4} - \frac{77070954725795011737342}{146160698785720231801}e^{3} - \frac{191130982112102415020358}{146160698785720231801}e^{2} + \frac{34494709716797879194797}{146160698785720231801}e + \frac{55548317469184965654924}{146160698785720231801}$
71 $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ $-\frac{1222202049124590363}{146160698785720231801}e^{14} - \frac{8769786405838115315}{146160698785720231801}e^{13} + \frac{22830195838851585076}{146160698785720231801}e^{12} + \frac{279368732843566597676}{146160698785720231801}e^{11} + \frac{105185824777768011255}{146160698785720231801}e^{10} - \frac{2943879624945985157463}{146160698785720231801}e^{9} - \frac{3646126751845311955386}{146160698785720231801}e^{8} + \frac{13100425744382304833626}{146160698785720231801}e^{7} + \frac{20825108864389688702889}{146160698785720231801}e^{6} - \frac{26255336816284073790876}{146160698785720231801}e^{5} - \frac{44977299123972488410557}{146160698785720231801}e^{4} + \frac{23424177169165865895974}{146160698785720231801}e^{3} + \frac{37753924665528492837986}{146160698785720231801}e^{2} - \frac{7407543430853749943572}{146160698785720231801}e - \frac{9641442313955229320572}{146160698785720231801}$
79 $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ $-\frac{4046290012619144808}{146160698785720231801}e^{14} - \frac{31249997344773165878}{146160698785720231801}e^{13} + \frac{64698811003988560083}{146160698785720231801}e^{12} + \frac{997177060254196614614}{146160698785720231801}e^{11} + \frac{735408602349985208425}{146160698785720231801}e^{10} - \frac{10541869829556032649947}{146160698785720231801}e^{9} - \frac{16959740901714724650443}{146160698785720231801}e^{8} + \frac{47215519372359323284018}{146160698785720231801}e^{7} + \frac{97180144135134633035910}{146160698785720231801}e^{6} - \frac{96261318475094611970309}{146160698785720231801}e^{5} - \frac{226726293742155896370435}{146160698785720231801}e^{4} + \frac{91845826486342961164406}{146160698785720231801}e^{3} + \frac{218055662471491068308264}{146160698785720231801}e^{2} - \frac{38356754409407226247848}{146160698785720231801}e - \frac{63234441790807289729180}{146160698785720231801}$
81 $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ $\phantom{-}\frac{1960765784412320297}{146160698785720231801}e^{14} + \frac{16124185532453503945}{146160698785720231801}e^{13} - \frac{25244883003023319025}{146160698785720231801}e^{12} - \frac{506226459725116509807}{146160698785720231801}e^{11} - \frac{551689534658613941076}{146160698785720231801}e^{10} + \frac{5187168841789348284686}{146160698785720231801}e^{9} + \frac{10293027793111448912389}{146160698785720231801}e^{8} - \frac{21950467293537052695206}{146160698785720231801}e^{7} - \frac{56465131308324727680125}{146160698785720231801}e^{6} + \frac{41033003495573435428030}{146160698785720231801}e^{5} + \frac{129054424658429776530473}{146160698785720231801}e^{4} - \frac{37527113798559272178296}{146160698785720231801}e^{3} - \frac{122190312884405780610052}{146160698785720231801}e^{2} + \frac{19462965490563796879636}{146160698785720231801}e + \frac{33148638577712233434602}{146160698785720231801}$
89 $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ $\phantom{-}\frac{1496069640723106321}{146160698785720231801}e^{14} + \frac{11136021048395828764}{146160698785720231801}e^{13} - \frac{26382005451277143938}{146160698785720231801}e^{12} - \frac{359302677050502634887}{146160698785720231801}e^{11} - \frac{195641193269344631983}{146160698785720231801}e^{10} + \frac{3879086121813906438563}{146160698785720231801}e^{9} + \frac{5505417019804336284815}{146160698785720231801}e^{8} - \frac{18049275425005460989057}{146160698785720231801}e^{7} - \frac{32765296296430057961504}{146160698785720231801}e^{6} + \frac{39225292695743255811798}{146160698785720231801}e^{5} + \frac{77856878568700046519170}{146160698785720231801}e^{4} - \frac{40601493932671690903193}{146160698785720231801}e^{3} - \frac{75410488764315240551325}{146160698785720231801}e^{2} + \frac{17279472480963750953738}{146160698785720231801}e + \frac{22376957005397198858840}{146160698785720231801}$
89 $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ $-\frac{1272105279941790990}{146160698785720231801}e^{14} - \frac{9636428259059892630}{146160698785720231801}e^{13} + \frac{20027980073132884481}{146160698785720231801}e^{12} + \frac{301041579769393420782}{146160698785720231801}e^{11} + \frac{230857158672138235543}{146160698785720231801}e^{10} - \frac{3048225198290755394819}{146160698785720231801}e^{9} - \frac{5124326496953631965340}{146160698785720231801}e^{8} + \frac{12498743621681127708311}{146160698785720231801}e^{7} + \frac{28017487577841051878285}{146160698785720231801}e^{6} - \frac{21245527096523137974085}{146160698785720231801}e^{5} - \frac{61056646287823647124021}{146160698785720231801}e^{4} + \frac{14682302338429931218060}{146160698785720231801}e^{3} + \frac{53695670414281837497866}{146160698785720231801}e^{2} - \frac{5778094081174951124512}{146160698785720231801}e - \frac{13332549588517996588618}{146160698785720231801}$
89 $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ $-\frac{1025394963863865481}{146160698785720231801}e^{14} - \frac{7582374539910630009}{146160698785720231801}e^{13} + \frac{17698119982499333855}{146160698785720231801}e^{12} + \frac{240651260489840681527}{146160698785720231801}e^{11} + \frac{139963998055383226309}{146160698785720231801}e^{10} - \frac{2515523548696496295588}{146160698785720231801}e^{9} - \frac{3712268450207662134340}{146160698785720231801}e^{8} + \frac{11001974180316784868916}{146160698785720231801}e^{7} + \frac{21264453940687682454510}{146160698785720231801}e^{6} - \frac{21384746113611487452819}{146160698785720231801}e^{5} - \frac{48359580037605419344502}{146160698785720231801}e^{4} + \frac{19099826530599826737832}{146160698785720231801}e^{3} + \frac{45190890295148001780184}{146160698785720231801}e^{2} - \frac{8068314805766348043962}{146160698785720231801}e - \frac{14131559106175732577058}{146160698785720231801}$
89 $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ $\phantom{-}\frac{1385992289472554048}{146160698785720231801}e^{14} + \frac{10584555717128081342}{146160698785720231801}e^{13} - \frac{24017766484522061212}{146160698785720231801}e^{12} - \frac{345814977941034742177}{146160698785720231801}e^{11} - \frac{204794975650422828944}{146160698785720231801}e^{10} + \frac{3819057050602118844675}{146160698785720231801}e^{9} + \frac{5554056242565595520650}{146160698785720231801}e^{8} - \frac{18427986344090366850240}{146160698785720231801}e^{7} - \frac{34082851899358280262686}{146160698785720231801}e^{6} + \frac{41822255027016059913595}{146160698785720231801}e^{5} + \frac{85408411196099471087318}{146160698785720231801}e^{4} - \frac{43659886899835382438344}{146160698785720231801}e^{3} - \frac{87892942039743356291312}{146160698785720231801}e^{2} + \frac{17494338948294912885086}{146160698785720231801}e + \frac{27186989243433674077090}{146160698785720231801}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$49$ $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ $-1$