Properties

Label 2.46.a
Level 2
Weight 46
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: \( k \) = \( 46 \)
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 \(M_{46}(\Gamma_0(2))\).

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

\(4q \) \(\mathstrut -\mathstrut 9904989360q^{3} \) \(\mathstrut +\mathstrut 70368744177664q^{4} \) \(\mathstrut -\mathstrut 105382171276200q^{5} \) \(\mathstrut +\mathstrut 543696821919154176q^{6} \) \(\mathstrut -\mathstrut 1661858231737805920q^{7} \) \(\mathstrut +\mathstrut 8962376138301500039412q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 9904989360q^{3} \) \(\mathstrut +\mathstrut 70368744177664q^{4} \) \(\mathstrut -\mathstrut 105382171276200q^{5} \) \(\mathstrut +\mathstrut 543696821919154176q^{6} \) \(\mathstrut -\mathstrut 1661858231737805920q^{7} \) \(\mathstrut +\mathstrut 8962376138301500039412q^{9} \) \(\mathstrut +\mathstrut 37327670467725203865600q^{10} \) \(\mathstrut +\mathstrut 392168665881251292269808q^{11} \) \(\mathstrut -\mathstrut 174250415589080967413760q^{12} \) \(\mathstrut +\mathstrut 9138633099697996407167480q^{13} \) \(\mathstrut +\mathstrut 73261256251509693084598272q^{14} \) \(\mathstrut +\mathstrut 1496580253913676729412274400q^{15} \) \(\mathstrut +\mathstrut 1237940039285380274899124224q^{16} \) \(\mathstrut -\mathstrut 5006992886561129117668330680q^{17} \) \(\mathstrut -\mathstrut 22606325752975403881731194880q^{18} \) \(\mathstrut -\mathstrut 128077534314696513630228811120q^{19} \) \(\mathstrut -\mathstrut 1853902762855422292603699200q^{20} \) \(\mathstrut +\mathstrut 479995496180181935365909381248q^{21} \) \(\mathstrut -\mathstrut 22663934163684306725193646080q^{22} \) \(\mathstrut +\mathstrut 3975175256193205056244738787040q^{23} \) \(\mathstrut +\mathstrut 9564815642959475269229887881216q^{24} \) \(\mathstrut +\mathstrut 22021988268168597447194339357500q^{25} \) \(\mathstrut -\mathstrut 57729053909565656316155101446144q^{26} \) \(\mathstrut -\mathstrut 557302881706926433863850723281120q^{27} \) \(\mathstrut -\mathstrut 29235719192175680197407507742720q^{28} \) \(\mathstrut +\mathstrut 1932951985237254271807151798827320q^{29} \) \(\mathstrut +\mathstrut 1164470447961241838885606208307200q^{30} \) \(\mathstrut +\mathstrut 5460601863143616678327168042247808q^{31} \) \(\mathstrut -\mathstrut 43544646620131760182008125963807040q^{33} \) \(\mathstrut -\mathstrut 34113947177503628204472621877690368q^{34} \) \(\mathstrut +\mathstrut 20710734226028729491402296893476800q^{35} \) \(\mathstrut +\mathstrut 157667788425034611331142660382523392q^{36} \) \(\mathstrut +\mathstrut 314766085045624019446836741178632920q^{37} \) \(\mathstrut -\mathstrut 217927140766564799696080911760097280q^{38} \) \(\mathstrut -\mathstrut 523833071014649150453174415139483296q^{39} \) \(\mathstrut +\mathstrut 656675323472874594786036856494489600q^{40} \) \(\mathstrut -\mathstrut 1440851727041043664349729399028639192q^{41} \) \(\mathstrut -\mathstrut 1438459282920399582205895494713999360q^{42} \) \(\mathstrut -\mathstrut 4353122265736039564851496142677697680q^{43} \) \(\mathstrut +\mathstrut 6899104130973390110132481917743792128q^{44} \) \(\mathstrut +\mathstrut 1434007796059617170200835837404721400q^{45} \) \(\mathstrut +\mathstrut 41998850788767486288261616839149223936q^{46} \) \(\mathstrut +\mathstrut 24106109182985243818670837833478623680q^{47} \) \(\mathstrut -\mathstrut 3065445729359918406607425128009564160q^{48} \) \(\mathstrut -\mathstrut 345714159146319375118971879495514492572q^{49} \) \(\mathstrut +\mathstrut 322973704396461180591214936090214400000q^{50} \) \(\mathstrut -\mathstrut 712620401216998563256255071407456802912q^{51} \) \(\mathstrut +\mathstrut 160768533681545224378408249732030791680q^{52} \) \(\mathstrut +\mathstrut 745597841971723828760410795662224134680q^{53} \) \(\mathstrut +\mathstrut 4266810021812428017028191591050520821760q^{54} \) \(\mathstrut -\mathstrut 2932269731766114076220348627372366402400q^{55} \) \(\mathstrut +\mathstrut 1288825649824193259214221064348108849152q^{56} \) \(\mathstrut -\mathstrut 16229922358819524465709884975101086384320q^{57} \) \(\mathstrut +\mathstrut 10461075445329320737119629288388836720640q^{58} \) \(\mathstrut -\mathstrut 14571880111406593515875947519203084494160q^{59} \) \(\mathstrut +\mathstrut 26328118257248737525522267541413979750400q^{60} \) \(\mathstrut -\mathstrut 4734195463547971403223183420705219205192q^{61} \) \(\mathstrut +\mathstrut 58048431121770441901375800272506784317440q^{62} \) \(\mathstrut -\mathstrut 42746862225971799438240431647179735487200q^{63} \) \(\mathstrut +\mathstrut 21778071482940061661655974875633165533184q^{64} \) \(\mathstrut -\mathstrut 154121743905347517289580253666025753959600q^{65} \) \(\mathstrut +\mathstrut 122391717144031641709191435226655439716352q^{66} \) \(\mathstrut -\mathstrut 179329174167042537403681756450852990986160q^{67} \) \(\mathstrut -\mathstrut 88083950383450879857536270522423055482880q^{68} \) \(\mathstrut +\mathstrut 410793972273322759100385112499872235581824q^{69} \) \(\mathstrut -\mathstrut 121490057475503510854143110277938911641600q^{70} \) \(\mathstrut +\mathstrut 550760420371852223644604518670515581698208q^{71} \) \(\mathstrut -\mathstrut 397694688427015923156692721142180431790080q^{72} \) \(\mathstrut +\mathstrut 1024605129549454751267558995998606802522280q^{73} \) \(\mathstrut -\mathstrut 2922550415278378473390627470670258921013248q^{74} \) \(\mathstrut +\mathstrut 3725910188767882164253032194962002039150000q^{75} \) \(\mathstrut -\mathstrut 2253163811774215365456080817182151194705920q^{76} \) \(\mathstrut -\mathstrut 32468545148351518030341904903922078090880q^{77} \) \(\mathstrut -\mathstrut 10246197789354863774261666808570264755896320q^{78} \) \(\mathstrut +\mathstrut 2744194767342556834734206641405857718982720q^{79} \) \(\mathstrut -\mathstrut 32614202312409425195017137162737103667200q^{80} \) \(\mathstrut +\mathstrut 38949457624282041606240457830903605203553124q^{81} \) \(\mathstrut -\mathstrut 9551184301678873439617882420843272355184640q^{82} \) \(\mathstrut +\mathstrut 89646158697289098884126697583968824307600q^{83} \) \(\mathstrut +\mathstrut 8444170069283530079136016735271959205511168q^{84} \) \(\mathstrut -\mathstrut 83993497878388479751550786423360628004405200q^{85} \) \(\mathstrut +\mathstrut 11513782324954011233506654854310825291677696q^{86} \) \(\mathstrut -\mathstrut 47929576933086582417452742130266734107086240q^{87} \) \(\mathstrut -\mathstrut 398708146305930069004859675363731864289280q^{88} \) \(\mathstrut -\mathstrut 58711455377158657966716122964002482591650840q^{89} \) \(\mathstrut +\mathstrut 406304650326774713727350815521354483027148800q^{90} \) \(\mathstrut -\mathstrut 13720430448725513731261681974914884553774912q^{91} \) \(\mathstrut +\mathstrut 69932022666109899464675302041188387405168640q^{92} \) \(\mathstrut -\mathstrut 113679078845005833868882341916702698658536960q^{93} \) \(\mathstrut +\mathstrut 201830938739784351396359727491617106335629312q^{94} \) \(\mathstrut -\mathstrut 1155023671775335018274991906461977129898244000q^{95} \) \(\mathstrut +\mathstrut 168266016271483530996380317923612478308089856q^{96} \) \(\mathstrut -\mathstrut 782649370621777826334195056133291722986286200q^{97} \) \(\mathstrut -\mathstrut 43206098978888925955090337553201565186129920q^{98} \) \(\mathstrut +\mathstrut 2162661876036681137607989489114307982625592624q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{46}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.46.a.a \(2\) \(25.651\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-8388608\) \(-69766206552\) \(-4\!\cdots\!00\) \(-9\!\cdots\!44\) \(+\) \(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b \(2\) \(25.651\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(8388608\) \(59861217192\) \(43\!\cdots\!00\) \(79\!\cdots\!24\) \(-\) \(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)

Decomposition of \(S_{46}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{46}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{46}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)