Properties

Label 4.4.19600.1-25.1-s
Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$
Dimension $20$
CM no
Base change yes

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Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 15x^{2} + 16x + 29\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$
Dimension: $20$
CM: no
Base change: yes
Newspace dimension: $62$

Hecke eigenvalues ($q$-expansion)

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

\(x^{20} - 174x^{18} + 12411x^{16} - 471702x^{14} + 10383433x^{12} - 134576452x^{10} + 1000446824x^{8} - 4019323448x^{6} + 8051575744x^{4} - 6304320768x^{2} + 24088464\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $-\frac{2294618142182220930976591}{162577965611317589525138438644}e^{18} + \frac{391974476552774636539280389}{162577965611317589525138438644}e^{16} - \frac{27233428994281374466656495293}{162577965611317589525138438644}e^{14} + \frac{995876463055147376241835742067}{162577965611317589525138438644}e^{12} - \frac{10331548842519293719440139838995}{81288982805658794762569219322}e^{10} + \frac{121589893786065535708987639163883}{81288982805658794762569219322}e^{8} - \frac{1523404872517883055402805915132521}{162577965611317589525138438644}e^{6} + \frac{1096349369930348910464407904622776}{40644491402829397381284609661}e^{4} - \frac{1137657265626944412600260173101618}{40644491402829397381284609661}e^{2} + \frac{4443733806668588508607810744609}{40644491402829397381284609661}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $\phantom{-}\frac{7731923176325262600216173}{650311862445270358100553754576}e^{18} - \frac{330199072461708862038996117}{162577965611317589525138438644}e^{16} + \frac{91765715798176614332851445453}{650311862445270358100553754576}e^{14} - \frac{209730603749032397471715753738}{40644491402829397381284609661}e^{12} + \frac{69625156158312757740121934072175}{650311862445270358100553754576}e^{10} - \frac{409689799494474505913428478544425}{325155931222635179050276877288}e^{8} + \frac{2566336636170892590204192256243969}{325155931222635179050276877288}e^{6} - \frac{3693246802216693519818250334717901}{162577965611317589525138438644}e^{4} + \frac{1915568633740772959255021369635315}{81288982805658794762569219322}e^{2} - \frac{7093353255251210370498127725229}{81288982805658794762569219322}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $\phantom{-}\frac{7731923176325262600216173}{650311862445270358100553754576}e^{18} - \frac{330199072461708862038996117}{162577965611317589525138438644}e^{16} + \frac{91765715798176614332851445453}{650311862445270358100553754576}e^{14} - \frac{209730603749032397471715753738}{40644491402829397381284609661}e^{12} + \frac{69625156158312757740121934072175}{650311862445270358100553754576}e^{10} - \frac{409689799494474505913428478544425}{325155931222635179050276877288}e^{8} + \frac{2566336636170892590204192256243969}{325155931222635179050276877288}e^{6} - \frac{3693246802216693519818250334717901}{162577965611317589525138438644}e^{4} + \frac{1915568633740772959255021369635315}{81288982805658794762569219322}e^{2} - \frac{7093353255251210370498127725229}{81288982805658794762569219322}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $\phantom{-}e$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $\phantom{-}\frac{34635906992759640786552853711}{797932655220346729389379456864752}e^{19} - \frac{1972227576549736304951787207651}{265977551740115576463126485621584}e^{17} + \frac{137027146329658781757589364924271}{265977551740115576463126485621584}e^{15} - \frac{5010895702942481709003672051058557}{265977551740115576463126485621584}e^{13} + \frac{311912235778222692487715946495051751}{797932655220346729389379456864752}e^{11} - \frac{3670874958550581173883773022294875851}{797932655220346729389379456864752}e^{9} + \frac{11498156622816749547648029493963940375}{398966327610173364694689728432376}e^{7} - \frac{16548876022054006488001803543627225167}{199483163805086682347344864216188}e^{5} + \frac{17165182752872017214958552450066740017}{199483163805086682347344864216188}e^{3} - \frac{8565074148426851486178606934174871}{33247193967514447057890810702698}e$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $\phantom{-}\frac{34635906992759640786552853711}{797932655220346729389379456864752}e^{19} - \frac{1972227576549736304951787207651}{265977551740115576463126485621584}e^{17} + \frac{137027146329658781757589364924271}{265977551740115576463126485621584}e^{15} - \frac{5010895702942481709003672051058557}{265977551740115576463126485621584}e^{13} + \frac{311912235778222692487715946495051751}{797932655220346729389379456864752}e^{11} - \frac{3670874958550581173883773022294875851}{797932655220346729389379456864752}e^{9} + \frac{11498156622816749547648029493963940375}{398966327610173364694689728432376}e^{7} - \frac{16548876022054006488001803543627225167}{199483163805086682347344864216188}e^{5} + \frac{17165182752872017214958552450066740017}{199483163805086682347344864216188}e^{3} - \frac{8565074148426851486178606934174871}{33247193967514447057890810702698}e$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $-1$
29 $[29, 29, w]$ $-\frac{6199169078288473510188312191}{77549689596598490203491035233188}e^{18} + \frac{705984324393057962044663934369}{51699793064398993468994023488792}e^{16} - \frac{16350285355293785950830532284041}{17233264354799664489664674496264}e^{14} + \frac{1793737026697880173341428241233311}{51699793064398993468994023488792}e^{12} - \frac{111655992990081071206168814045236375}{155099379193196980406982070466376}e^{10} + \frac{1314108252962398318188624953445656953}{155099379193196980406982070466376}e^{8} - \frac{8232757452197381127307442716184699351}{155099379193196980406982070466376}e^{6} + \frac{5925463172941047081472471676787958715}{38774844798299245101745517616594}e^{4} - \frac{6149384071591965987278493595449426337}{38774844798299245101745517616594}e^{2} + \frac{7913945456882181736708685912772053}{12924948266099748367248505872198}$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $-\frac{7902410904474611229057224683}{310198758386393960813964140932752}e^{18} + \frac{224988174970907853571476886405}{51699793064398993468994023488792}e^{16} - \frac{10421177427278333466448022723567}{34466528709599328979329348992528}e^{14} + \frac{571628626042795169894461979472635}{51699793064398993468994023488792}e^{12} - \frac{71163171022996916507995087886772433}{310198758386393960813964140932752}e^{10} + \frac{209373495640850003290848591809957569}{77549689596598490203491035233188}e^{8} - \frac{2623139869669375240583570600421106363}{155099379193196980406982070466376}e^{6} + \frac{3775181548032541174162645210188447659}{77549689596598490203491035233188}e^{4} - \frac{979123813499025378754386756420535822}{19387422399149622550872758808297}e^{2} + \frac{2480918515842067366642951002458377}{12924948266099748367248505872198}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $-\frac{6199169078288473510188312191}{77549689596598490203491035233188}e^{18} + \frac{705984324393057962044663934369}{51699793064398993468994023488792}e^{16} - \frac{16350285355293785950830532284041}{17233264354799664489664674496264}e^{14} + \frac{1793737026697880173341428241233311}{51699793064398993468994023488792}e^{12} - \frac{111655992990081071206168814045236375}{155099379193196980406982070466376}e^{10} + \frac{1314108252962398318188624953445656953}{155099379193196980406982070466376}e^{8} - \frac{8232757452197381127307442716184699351}{155099379193196980406982070466376}e^{6} + \frac{5925463172941047081472471676787958715}{38774844798299245101745517616594}e^{4} - \frac{6149384071591965987278493595449426337}{38774844798299245101745517616594}e^{2} + \frac{7913945456882181736708685912772053}{12924948266099748367248505872198}$
29 $[29, 29, -w + 1]$ $-\frac{7902410904474611229057224683}{310198758386393960813964140932752}e^{18} + \frac{224988174970907853571476886405}{51699793064398993468994023488792}e^{16} - \frac{10421177427278333466448022723567}{34466528709599328979329348992528}e^{14} + \frac{571628626042795169894461979472635}{51699793064398993468994023488792}e^{12} - \frac{71163171022996916507995087886772433}{310198758386393960813964140932752}e^{10} + \frac{209373495640850003290848591809957569}{77549689596598490203491035233188}e^{8} - \frac{2623139869669375240583570600421106363}{155099379193196980406982070466376}e^{6} + \frac{3775181548032541174162645210188447659}{77549689596598490203491035233188}e^{4} - \frac{979123813499025378754386756420535822}{19387422399149622550872758808297}e^{2} + \frac{2480918515842067366642951002458377}{12924948266099748367248505872198}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{660113975490376139935024928893}{14096810242226125552545703737943952}e^{19} - \frac{112763875801339341507259131119581}{14096810242226125552545703737943952}e^{17} + \frac{7834630583138584139611820980928287}{14096810242226125552545703737943952}e^{15} - \frac{286500617245625663199748873257477755}{14096810242226125552545703737943952}e^{13} + \frac{5944545060001261006272676366388199297}{14096810242226125552545703737943952}e^{11} - \frac{69960292358131240801719975004723581783}{14096810242226125552545703737943952}e^{9} + \frac{219131560645106917595106307835733591597}{7048405121113062776272851868971976}e^{7} - \frac{315389997272390007299649248477067006959}{3524202560556531388136425934485988}e^{5} + \frac{327219736975090542262766235860912400849}{3524202560556531388136425934485988}e^{3} - \frac{605512030758086740360709604125130087}{1762101280278265694068212967242994}e$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $-\frac{163830616945862641950359891973}{14096810242226125552545703737943952}e^{19} + \frac{1749122263440679840377989054546}{881050640139132847034106483621497}e^{17} - \frac{1944371839266452576430213574909077}{14096810242226125552545703737943952}e^{15} + \frac{8887535219075704594034873198317569}{1762101280278265694068212967242994}e^{13} - \frac{1475160477193326600799991497839351407}{14096810242226125552545703737943952}e^{11} + \frac{8679560619806755296888238920525574859}{7048405121113062776272851868971976}e^{9} - \frac{54361847302465440775657339987252574383}{7048405121113062776272851868971976}e^{7} + \frac{78206421212101040187052803273260434257}{3524202560556531388136425934485988}e^{5} - \frac{40525070975125026755069510160724605715}{1762101280278265694068212967242994}e^{3} + \frac{96485125148785949197669275738409527}{1762101280278265694068212967242994}e$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $\phantom{-}\frac{660113975490376139935024928893}{14096810242226125552545703737943952}e^{19} - \frac{112763875801339341507259131119581}{14096810242226125552545703737943952}e^{17} + \frac{7834630583138584139611820980928287}{14096810242226125552545703737943952}e^{15} - \frac{286500617245625663199748873257477755}{14096810242226125552545703737943952}e^{13} + \frac{5944545060001261006272676366388199297}{14096810242226125552545703737943952}e^{11} - \frac{69960292358131240801719975004723581783}{14096810242226125552545703737943952}e^{9} + \frac{219131560645106917595106307835733591597}{7048405121113062776272851868971976}e^{7} - \frac{315389997272390007299649248477067006959}{3524202560556531388136425934485988}e^{5} + \frac{327219736975090542262766235860912400849}{3524202560556531388136425934485988}e^{3} - \frac{605512030758086740360709604125130087}{1762101280278265694068212967242994}e$
31 $[31, 31, -w + 3]$ $-\frac{163830616945862641950359891973}{14096810242226125552545703737943952}e^{19} + \frac{1749122263440679840377989054546}{881050640139132847034106483621497}e^{17} - \frac{1944371839266452576430213574909077}{14096810242226125552545703737943952}e^{15} + \frac{8887535219075704594034873198317569}{1762101280278265694068212967242994}e^{13} - \frac{1475160477193326600799991497839351407}{14096810242226125552545703737943952}e^{11} + \frac{8679560619806755296888238920525574859}{7048405121113062776272851868971976}e^{9} - \frac{54361847302465440775657339987252574383}{7048405121113062776272851868971976}e^{7} + \frac{78206421212101040187052803273260434257}{3524202560556531388136425934485988}e^{5} - \frac{40525070975125026755069510160724605715}{1762101280278265694068212967242994}e^{3} + \frac{96485125148785949197669275738409527}{1762101280278265694068212967242994}e$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $-\frac{25820574892282680789522037}{162577965611317589525138438644}e^{18} + \frac{2205412926972830387007071987}{81288982805658794762569219322}e^{16} - \frac{153229614404598553875173507927}{81288982805658794762569219322}e^{14} + \frac{2801728945786744132086421408764}{40644491402829397381284609661}e^{12} - \frac{116267697658590277067563406603361}{81288982805658794762569219322}e^{10} + \frac{1368385421951174992994620898611313}{81288982805658794762569219322}e^{8} - \frac{17145548213901845214904269952496871}{162577965611317589525138438644}e^{6} + \frac{12340245882002271286151145568221876}{40644491402829397381284609661}e^{4} - \frac{12806248278590278980297638804686602}{40644491402829397381284609661}e^{2} + \frac{49233104138908779949500967159679}{40644491402829397381284609661}$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $\phantom{-}\frac{6183358701447582271202649669413}{126871292180035129972911333641495568}e^{19} - \frac{352095198182962039285630765303987}{42290430726678376657637111213831856}e^{17} + \frac{8154477460388257448834697824479943}{14096810242226125552545703737943952}e^{15} - \frac{894618911300747289339142195825915685}{42290430726678376657637111213831856}e^{13} + \frac{55689700765698612467505711877850413589}{126871292180035129972911333641495568}e^{11} - \frac{655463147975898317589023510082883736927}{126871292180035129972911333641495568}e^{9} + \frac{2053451193968999660256087778677840023531}{63435646090017564986455666820747784}e^{7} - \frac{2956886840356563585906485751340055361625}{31717823045008782493227833410373892}e^{5} + \frac{3072485847704702434164612894096603206429}{31717823045008782493227833410373892}e^{3} - \frac{3146972649270900547915184608715401073}{5286303840834797082204638901728982}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{4626580442588694168865326387673}{126871292180035129972911333641495568}e^{19} - \frac{263442831101793816057823287283679}{42290430726678376657637111213831856}e^{17} + \frac{6101100534391304713489948199900867}{14096810242226125552545703737943952}e^{15} - \frac{669310538071799552171597434264554169}{42290430726678376657637111213831856}e^{13} + \frac{41660739589598992990553399891262331393}{126871292180035129972911333641495568}e^{11} - \frac{490266393695991640673944371581051008099}{126871292180035129972911333641495568}e^{9} + \frac{1535416611243253329988283022582855596563}{63435646090017564986455666820747784}e^{7} - \frac{2209086593870597318959809187994678202125}{31717823045008782493227833410373892}e^{5} + \frac{2289024372009207052842720735558106997281}{31717823045008782493227833410373892}e^{3} - \frac{577503065089656198657848137282512145}{5286303840834797082204638901728982}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $\phantom{-}\frac{6183358701447582271202649669413}{126871292180035129972911333641495568}e^{19} - \frac{352095198182962039285630765303987}{42290430726678376657637111213831856}e^{17} + \frac{8154477460388257448834697824479943}{14096810242226125552545703737943952}e^{15} - \frac{894618911300747289339142195825915685}{42290430726678376657637111213831856}e^{13} + \frac{55689700765698612467505711877850413589}{126871292180035129972911333641495568}e^{11} - \frac{655463147975898317589023510082883736927}{126871292180035129972911333641495568}e^{9} + \frac{2053451193968999660256087778677840023531}{63435646090017564986455666820747784}e^{7} - \frac{2956886840356563585906485751340055361625}{31717823045008782493227833410373892}e^{5} + \frac{3072485847704702434164612894096603206429}{31717823045008782493227833410373892}e^{3} - \frac{3146972649270900547915184608715401073}{5286303840834797082204638901728982}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25,5,-\frac{4}{23}w^{3}+\frac{6}{23}w^{2}+\frac{40}{23}w-\frac{21}{23}]$ $1$