Properties

Label 2.44.a
Level 2
Weight 44
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 11
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 44 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_0(2))\).

Total New Old
Modular forms 12 4 8
Cusp forms 10 4 6
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(2\)Dim.
\(+\)\(2\)
\(-\)\(2\)

Trace form

\(4q \) \(\mathstrut -\mathstrut 35323265040q^{3} \) \(\mathstrut +\mathstrut 17592186044416q^{4} \) \(\mathstrut -\mathstrut 445983369680520q^{5} \) \(\mathstrut -\mathstrut 19629349162450944q^{6} \) \(\mathstrut +\mathstrut 952409902196202080q^{7} \) \(\mathstrut +\mathstrut 57392344928214127188q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 35323265040q^{3} \) \(\mathstrut +\mathstrut 17592186044416q^{4} \) \(\mathstrut -\mathstrut 445983369680520q^{5} \) \(\mathstrut -\mathstrut 19629349162450944q^{6} \) \(\mathstrut +\mathstrut 952409902196202080q^{7} \) \(\mathstrut +\mathstrut 57392344928214127188q^{9} \) \(\mathstrut +\mathstrut 736817688890793000960q^{10} \) \(\mathstrut -\mathstrut 53505666230187039126192q^{11} \) \(\mathstrut -\mathstrut 155353362569973895004160q^{12} \) \(\mathstrut -\mathstrut 3170092445107476877943080q^{13} \) \(\mathstrut -\mathstrut 2930413749959980348342272q^{14} \) \(\mathstrut -\mathstrut 39896100567148303597839840q^{15} \) \(\mathstrut +\mathstrut 77371252455336267181195264q^{16} \) \(\mathstrut +\mathstrut 275811531610294198491666120q^{17} \) \(\mathstrut +\mathstrut 2155446423566237915236270080q^{18} \) \(\mathstrut +\mathstrut 704368595409646764116849840q^{19} \) \(\mathstrut -\mathstrut 1961455603033816441112494080q^{20} \) \(\mathstrut -\mathstrut 71943252193711849582874093952q^{21} \) \(\mathstrut -\mathstrut 63480896917120890827786158080q^{22} \) \(\mathstrut +\mathstrut 267622990007463399665328694560q^{23} \) \(\mathstrut -\mathstrut 86330790599159598780751282176q^{24} \) \(\mathstrut +\mathstrut 2883522820368023310220104607900q^{25} \) \(\mathstrut +\mathstrut 309677544891030919403091787776q^{26} \) \(\mathstrut -\mathstrut 13660960708029142515089178825120q^{27} \) \(\mathstrut +\mathstrut 4188743047494908425223347896320q^{28} \) \(\mathstrut -\mathstrut 38644798233978054156037925733480q^{29} \) \(\mathstrut +\mathstrut 8988615448994818274005163704320q^{30} \) \(\mathstrut +\mathstrut 202517590352351068698084253267328q^{31} \) \(\mathstrut +\mathstrut 698603125139732151618674183490240q^{33} \) \(\mathstrut -\mathstrut 860904569326544750263603436716032q^{34} \) \(\mathstrut -\mathstrut 3325520912837045799202976122441920q^{35} \) \(\mathstrut +\mathstrut 252414202375609491412627910295552q^{36} \) \(\mathstrut -\mathstrut 1007806155266724596382724999945480q^{37} \) \(\mathstrut +\mathstrut 3685618436761385576387510041313280q^{38} \) \(\mathstrut +\mathstrut 34627230647677526261318633218835616q^{39} \) \(\mathstrut +\mathstrut 3240558465945864657539990122659840q^{40} \) \(\mathstrut +\mathstrut 14769056217421573842182424655114728q^{41} \) \(\mathstrut -\mathstrut 188529371232675648676832840578498560q^{42} \) \(\mathstrut -\mathstrut 50656152082275083325922323570825520q^{43} \) \(\mathstrut -\mathstrut 235320408687969219594308666385235968q^{44} \) \(\mathstrut +\mathstrut 813851237061199242360170633473196760q^{45} \) \(\mathstrut -\mathstrut 401162053228680963277901151835521024q^{46} \) \(\mathstrut +\mathstrut 1795871719777727412019789817026927680q^{47} \) \(\mathstrut -\mathstrut 683251314239148431991403503566192640q^{48} \) \(\mathstrut +\mathstrut 2472588624099381815176131582897177252q^{49} \) \(\mathstrut -\mathstrut 14094510821977045744752591014933299200q^{50} \) \(\mathstrut +\mathstrut 9366222065014568589261957669399307488q^{51} \) \(\mathstrut -\mathstrut 13942214018082087317341913445899960320q^{52} \) \(\mathstrut +\mathstrut 34930183704299684660043854347335201720q^{53} \) \(\mathstrut -\mathstrut 54991919905881001033766855194737377280q^{54} \) \(\mathstrut +\mathstrut 101675970194038744959268516881965777760q^{55} \) \(\mathstrut -\mathstrut 12888095969102680990651131959640588288q^{56} \) \(\mathstrut +\mathstrut 24725309490521092416268712856158940480q^{57} \) \(\mathstrut -\mathstrut 224221408455435359075502788567724195840q^{58} \) \(\mathstrut +\mathstrut 74517661892831252610921679030012874640q^{59} \) \(\mathstrut -\mathstrut 175464905906000912317031679022973583360q^{60} \) \(\mathstrut +\mathstrut 95466819219187169456508921216701652248q^{61} \) \(\mathstrut -\mathstrut 256066710492626982167265418768715612160q^{62} \) \(\mathstrut +\mathstrut 1302503682143077872333511602225242757600q^{63} \) \(\mathstrut +\mathstrut 340282366920938463463374607431768211456q^{64} \) \(\mathstrut -\mathstrut 1140879441958849707741225198393647217840q^{65} \) \(\mathstrut +\mathstrut 2758089365183515747873923781071955034112q^{66} \) \(\mathstrut -\mathstrut 5185823154883915148339698804696290802960q^{67} \) \(\mathstrut +\mathstrut 1213031944320905010647284238286040596480q^{68} \) \(\mathstrut -\mathstrut 13169724835217980176395670977192312083584q^{69} \) \(\mathstrut +\mathstrut 13750686399482936758591003632374812508160q^{70} \) \(\mathstrut +\mathstrut 6078131343463252822749802888112407049568q^{71} \) \(\mathstrut +\mathstrut 9479753623037087268551680109182262968320q^{72} \) \(\mathstrut -\mathstrut 11299472539399729498004578793488644374680q^{73} \) \(\mathstrut +\mathstrut 16306213923786421705403162747840986349568q^{74} \) \(\mathstrut +\mathstrut 968840833644049096432036826739720166800q^{75} \) \(\mathstrut +\mathstrut 3097845843572621900589154698591060623360q^{76} \) \(\mathstrut -\mathstrut 122687760481577524751229519037503537559680q^{77} \) \(\mathstrut +\mathstrut 5665681380473715909273979796512592363520q^{78} \) \(\mathstrut +\mathstrut 39481139269211124080055934235826831819200q^{79} \) \(\mathstrut -\mathstrut 8626572971608268796564758456927854264320q^{80} \) \(\mathstrut +\mathstrut 303693792362524627388345705941115534711844q^{81} \) \(\mathstrut -\mathstrut 276362461442393760174426915844135311114240q^{82} \) \(\mathstrut +\mathstrut 450113087170899479515222133277261850695600q^{83} \) \(\mathstrut -\mathstrut 316409769308029594425462246614498707243008q^{84} \) \(\mathstrut +\mathstrut 339447401278646006771627630621380418317680q^{85} \) \(\mathstrut -\mathstrut 1089531960634141917764113636419993530793984q^{86} \) \(\mathstrut +\mathstrut 63269631265006087376268943554864452768160q^{87} \) \(\mathstrut -\mathstrut 279191937208096203349737387043928219320320q^{88} \) \(\mathstrut +\mathstrut 473243058306814632719521085066228455846440q^{89} \) \(\mathstrut -\mathstrut 42617612448701427992575832218399125012480q^{90} \) \(\mathstrut +\mathstrut 27907556672811409832272913003692321235008q^{91} \) \(\mathstrut +\mathstrut 1177018357493545059819073626342986864394240q^{92} \) \(\mathstrut +\mathstrut 3376287307445883190884526599190714638543360q^{93} \) \(\mathstrut +\mathstrut 3930274486025559007941997987062303820873728q^{94} \) \(\mathstrut -\mathstrut 9878276980119994764350873096834160483420000q^{95} \) \(\mathstrut -\mathstrut 379686832395483875172155628806131421282304q^{96} \) \(\mathstrut -\mathstrut 5934740187101728628006412969339693653467000q^{97} \) \(\mathstrut +\mathstrut 7327603468103810611042817664861329078353920q^{98} \) \(\mathstrut -\mathstrut 15605924803061079239520118761603262248845424q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.44.a.a \(2\) \(23.422\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-4194304\) \(-12981630984\) \(-3\!\cdots\!00\) \(11\!\cdots\!08\) \(+\) \(q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots\)
2.44.a.b \(2\) \(23.422\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(4194304\) \(-22341634056\) \(-4\!\cdots\!20\) \(-2\!\cdots\!28\) \(-\) \(q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots\)

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{44}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)