Properties

Label 2.46.a
Level 2
Weight 46
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 2
Sturm bound 11
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 46 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{46}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 4194304 T )^{2} \))(\( ( 1 - 4194304 T )^{2} \))
$3$ (\( 1 + 69766206552 T + \)\(17\!\cdots\!62\)\( T^{2} + \)\(20\!\cdots\!36\)\( T^{3} + \)\(87\!\cdots\!49\)\( T^{4} \))(\( 1 - 59861217192 T + \)\(38\!\cdots\!02\)\( T^{2} - \)\(17\!\cdots\!56\)\( T^{3} + \)\(87\!\cdots\!49\)\( T^{4} \))
$5$ (\( 1 + 4502496162681300 T + \)\(52\!\cdots\!50\)\( T^{2} + \)\(12\!\cdots\!00\)\( T^{3} + \)\(80\!\cdots\!25\)\( T^{4} \))(\( 1 - 4397113991405100 T + \)\(13\!\cdots\!50\)\( T^{2} - \)\(12\!\cdots\!00\)\( T^{3} + \)\(80\!\cdots\!25\)\( T^{4} \))
$7$ (\( 1 + 9564351425209104944 T + \)\(23\!\cdots\!98\)\( T^{2} + \)\(10\!\cdots\!08\)\( T^{3} + \)\(11\!\cdots\!49\)\( T^{4} \))(\( 1 - 7902493193471299024 T + \)\(22\!\cdots\!58\)\( T^{2} - \)\(84\!\cdots\!68\)\( T^{3} + \)\(11\!\cdots\!49\)\( T^{4} \))
$11$ (\( 1 - \)\(19\!\cdots\!64\)\( T + \)\(11\!\cdots\!26\)\( T^{2} - \)\(14\!\cdots\!64\)\( T^{3} + \)\(53\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(19\!\cdots\!44\)\( T + \)\(14\!\cdots\!86\)\( T^{2} - \)\(14\!\cdots\!44\)\( T^{3} + \)\(53\!\cdots\!01\)\( T^{4} \))
$13$ (\( 1 - \)\(11\!\cdots\!08\)\( T + \)\(21\!\cdots\!02\)\( T^{2} - \)\(15\!\cdots\!44\)\( T^{3} + \)\(17\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(23\!\cdots\!28\)\( T + \)\(10\!\cdots\!82\)\( T^{2} + \)\(31\!\cdots\!04\)\( T^{3} + \)\(17\!\cdots\!49\)\( T^{4} \))
$17$ (\( 1 - \)\(15\!\cdots\!56\)\( T + \)\(47\!\cdots\!98\)\( T^{2} - \)\(36\!\cdots\!92\)\( T^{3} + \)\(55\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(65\!\cdots\!36\)\( T + \)\(32\!\cdots\!38\)\( T^{2} + \)\(15\!\cdots\!52\)\( T^{3} + \)\(55\!\cdots\!49\)\( T^{4} \))
$19$ (\( 1 + \)\(38\!\cdots\!00\)\( T + \)\(26\!\cdots\!98\)\( T^{2} + \)\(13\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!01\)\( T^{4} \))(\( 1 + \)\(90\!\cdots\!20\)\( T + \)\(70\!\cdots\!98\)\( T^{2} + \)\(31\!\cdots\!80\)\( T^{3} + \)\(12\!\cdots\!01\)\( T^{4} \))
$23$ (\( 1 + \)\(30\!\cdots\!72\)\( T + \)\(29\!\cdots\!82\)\( T^{2} + \)\(57\!\cdots\!96\)\( T^{3} + \)\(35\!\cdots\!49\)\( T^{4} \))(\( 1 - \)\(69\!\cdots\!12\)\( T + \)\(38\!\cdots\!22\)\( T^{2} - \)\(13\!\cdots\!16\)\( T^{3} + \)\(35\!\cdots\!49\)\( T^{4} \))
$29$ (\( 1 + \)\(28\!\cdots\!20\)\( T + \)\(73\!\cdots\!98\)\( T^{2} + \)\(18\!\cdots\!80\)\( T^{3} + \)\(41\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(22\!\cdots\!40\)\( T + \)\(24\!\cdots\!98\)\( T^{2} - \)\(14\!\cdots\!60\)\( T^{3} + \)\(41\!\cdots\!01\)\( T^{4} \))
$31$ (\( 1 + \)\(41\!\cdots\!76\)\( T + \)\(23\!\cdots\!46\)\( T^{2} + \)\(54\!\cdots\!76\)\( T^{3} + \)\(16\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(96\!\cdots\!84\)\( T + \)\(46\!\cdots\!66\)\( T^{2} - \)\(12\!\cdots\!84\)\( T^{3} + \)\(16\!\cdots\!01\)\( T^{4} \))
$37$ (\( 1 - \)\(50\!\cdots\!16\)\( T + \)\(13\!\cdots\!78\)\( T^{2} - \)\(18\!\cdots\!12\)\( T^{3} + \)\(13\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(19\!\cdots\!96\)\( T + \)\(82\!\cdots\!18\)\( T^{2} + \)\(70\!\cdots\!72\)\( T^{3} + \)\(13\!\cdots\!49\)\( T^{4} \))
$41$ (\( 1 - \)\(41\!\cdots\!84\)\( T + \)\(47\!\cdots\!66\)\( T^{2} - \)\(15\!\cdots\!84\)\( T^{3} + \)\(14\!\cdots\!01\)\( T^{4} \))(\( 1 + \)\(18\!\cdots\!76\)\( T + \)\(63\!\cdots\!46\)\( T^{2} + \)\(69\!\cdots\!76\)\( T^{3} + \)\(14\!\cdots\!01\)\( T^{4} \))
$43$ (\( 1 + \)\(35\!\cdots\!52\)\( T + \)\(67\!\cdots\!62\)\( T^{2} + \)\(11\!\cdots\!36\)\( T^{3} + \)\(10\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(80\!\cdots\!28\)\( T + \)\(35\!\cdots\!82\)\( T^{2} + \)\(25\!\cdots\!04\)\( T^{3} + \)\(10\!\cdots\!49\)\( T^{4} \))
$47$ (\( 1 + \)\(12\!\cdots\!24\)\( T + \)\(17\!\cdots\!58\)\( T^{2} + \)\(21\!\cdots\!68\)\( T^{3} + \)\(30\!\cdots\!49\)\( T^{4} \))(\( 1 - \)\(36\!\cdots\!04\)\( T + \)\(38\!\cdots\!18\)\( T^{2} - \)\(63\!\cdots\!28\)\( T^{3} + \)\(30\!\cdots\!49\)\( T^{4} \))
$53$ (\( 1 - \)\(14\!\cdots\!68\)\( T + \)\(12\!\cdots\!42\)\( T^{2} - \)\(55\!\cdots\!24\)\( T^{3} + \)\(15\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(66\!\cdots\!88\)\( T + \)\(20\!\cdots\!22\)\( T^{2} + \)\(26\!\cdots\!84\)\( T^{3} + \)\(15\!\cdots\!49\)\( T^{4} \))
$59$ (\( 1 + \)\(14\!\cdots\!40\)\( T + \)\(14\!\cdots\!98\)\( T^{2} + \)\(70\!\cdots\!60\)\( T^{3} + \)\(23\!\cdots\!01\)\( T^{4} \))(\( 1 + \)\(14\!\cdots\!20\)\( T + \)\(53\!\cdots\!98\)\( T^{2} + \)\(71\!\cdots\!80\)\( T^{3} + \)\(23\!\cdots\!01\)\( T^{4} \))
$61$ (\( 1 + \)\(21\!\cdots\!56\)\( T + \)\(37\!\cdots\!86\)\( T^{2} + \)\(47\!\cdots\!56\)\( T^{3} + \)\(47\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(16\!\cdots\!64\)\( T + \)\(42\!\cdots\!26\)\( T^{2} - \)\(36\!\cdots\!64\)\( T^{3} + \)\(47\!\cdots\!01\)\( T^{4} \))
$67$ (\( 1 + \)\(96\!\cdots\!84\)\( T + \)\(28\!\cdots\!78\)\( T^{2} + \)\(14\!\cdots\!88\)\( T^{3} + \)\(22\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(82\!\cdots\!76\)\( T + \)\(22\!\cdots\!58\)\( T^{2} + \)\(12\!\cdots\!32\)\( T^{3} + \)\(22\!\cdots\!49\)\( T^{4} \))
$71$ (\( 1 - \)\(44\!\cdots\!44\)\( T + \)\(35\!\cdots\!86\)\( T^{2} - \)\(89\!\cdots\!44\)\( T^{3} + \)\(41\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(11\!\cdots\!64\)\( T + \)\(23\!\cdots\!26\)\( T^{2} - \)\(22\!\cdots\!64\)\( T^{3} + \)\(41\!\cdots\!01\)\( T^{4} \))
$73$ (\( 1 + \)\(34\!\cdots\!52\)\( T + \)\(12\!\cdots\!62\)\( T^{2} + \)\(24\!\cdots\!36\)\( T^{3} + \)\(50\!\cdots\!49\)\( T^{4} \))(\( 1 - \)\(13\!\cdots\!32\)\( T + \)\(15\!\cdots\!42\)\( T^{2} - \)\(96\!\cdots\!76\)\( T^{3} + \)\(50\!\cdots\!49\)\( T^{4} \))
$79$ (\( 1 + \)\(62\!\cdots\!80\)\( T - \)\(27\!\cdots\!02\)\( T^{2} + \)\(15\!\cdots\!20\)\( T^{3} + \)\(61\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(33\!\cdots\!00\)\( T + \)\(51\!\cdots\!98\)\( T^{2} - \)\(83\!\cdots\!00\)\( T^{3} + \)\(61\!\cdots\!01\)\( T^{4} \))
$83$ (\( 1 - \)\(96\!\cdots\!48\)\( T + \)\(40\!\cdots\!62\)\( T^{2} - \)\(21\!\cdots\!64\)\( T^{3} + \)\(52\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(95\!\cdots\!48\)\( T + \)\(32\!\cdots\!62\)\( T^{2} + \)\(21\!\cdots\!64\)\( T^{3} + \)\(52\!\cdots\!49\)\( T^{4} \))
$89$ (\( 1 + \)\(12\!\cdots\!20\)\( T + \)\(14\!\cdots\!98\)\( T^{2} + \)\(66\!\cdots\!80\)\( T^{3} + \)\(27\!\cdots\!01\)\( T^{4} \))(\( 1 - \)\(67\!\cdots\!80\)\( T + \)\(11\!\cdots\!98\)\( T^{2} - \)\(35\!\cdots\!20\)\( T^{3} + \)\(27\!\cdots\!01\)\( T^{4} \))
$97$ (\( 1 - \)\(47\!\cdots\!36\)\( T + \)\(47\!\cdots\!38\)\( T^{2} - \)\(12\!\cdots\!52\)\( T^{3} + \)\(64\!\cdots\!49\)\( T^{4} \))(\( 1 + \)\(82\!\cdots\!36\)\( T + \)\(67\!\cdots\!38\)\( T^{2} + \)\(21\!\cdots\!52\)\( T^{3} + \)\(64\!\cdots\!49\)\( T^{4} \))
show more
show less