Properties

Label 3.24.a
Level 3
Weight 24
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 24 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(3))\).

Total New Old
Modular forms 9 3 6
Cusp forms 7 3 4
Eisenstein series 2 0 2

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

\(3\)Dim.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut -\mathstrut 114q^{2} \) \(\mathstrut -\mathstrut 177147q^{3} \) \(\mathstrut -\mathstrut 13574940q^{4} \) \(\mathstrut -\mathstrut 95672550q^{5} \) \(\mathstrut +\mathstrut 419838390q^{6} \) \(\mathstrut -\mathstrut 1935652584q^{7} \) \(\mathstrut -\mathstrut 14917581480q^{8} \) \(\mathstrut +\mathstrut 94143178827q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 114q^{2} \) \(\mathstrut -\mathstrut 177147q^{3} \) \(\mathstrut -\mathstrut 13574940q^{4} \) \(\mathstrut -\mathstrut 95672550q^{5} \) \(\mathstrut +\mathstrut 419838390q^{6} \) \(\mathstrut -\mathstrut 1935652584q^{7} \) \(\mathstrut -\mathstrut 14917581480q^{8} \) \(\mathstrut +\mathstrut 94143178827q^{9} \) \(\mathstrut +\mathstrut 572751502740q^{10} \) \(\mathstrut +\mathstrut 40709186364q^{11} \) \(\mathstrut -\mathstrut 116475569676q^{12} \) \(\mathstrut +\mathstrut 2270690219922q^{13} \) \(\mathstrut +\mathstrut 32964234173376q^{14} \) \(\mathstrut -\mathstrut 364021141770q^{15} \) \(\mathstrut -\mathstrut 11006037260016q^{16} \) \(\mathstrut -\mathstrut 216877221851274q^{17} \) \(\mathstrut -\mathstrut 3577440795426q^{18} \) \(\mathstrut -\mathstrut 227376967262268q^{19} \) \(\mathstrut -\mathstrut 244823793603240q^{20} \) \(\mathstrut -\mathstrut 267797508894072q^{21} \) \(\mathstrut -\mathstrut 1226005562809368q^{22} \) \(\mathstrut +\mathstrut 10132363972083192q^{23} \) \(\mathstrut -\mathstrut 3553802567592264q^{24} \) \(\mathstrut +\mathstrut 5277240952025925q^{25} \) \(\mathstrut -\mathstrut 3363765742994124q^{26} \) \(\mathstrut -\mathstrut 5559060566555523q^{27} \) \(\mathstrut -\mathstrut 30242279289441792q^{28} \) \(\mathstrut +\mathstrut 133572946358500914q^{29} \) \(\mathstrut -\mathstrut 120989288986150140q^{30} \) \(\mathstrut -\mathstrut 363623347093854288q^{31} \) \(\mathstrut +\mathstrut 377929267417298016q^{32} \) \(\mathstrut -\mathstrut 513236585375675964q^{33} \) \(\mathstrut -\mathstrut 20891435156331300q^{34} \) \(\mathstrut +\mathstrut 2270395510722400080q^{35} \) \(\mathstrut -\mathstrut 425996001328598460q^{36} \) \(\mathstrut -\mathstrut 1298352381660014934q^{37} \) \(\mathstrut +\mathstrut 2692949270003591640q^{38} \) \(\mathstrut -\mathstrut 3314884195686105378q^{39} \) \(\mathstrut -\mathstrut 5700604079830875120q^{40} \) \(\mathstrut +\mathstrut 10769751186787426542q^{41} \) \(\mathstrut -\mathstrut 6528376395623524032q^{42} \) \(\mathstrut -\mathstrut 3608756663906114148q^{43} \) \(\mathstrut +\mathstrut 3808747584420013488q^{44} \) \(\mathstrut -\mathstrut 3002305994495032950q^{45} \) \(\mathstrut -\mathstrut 7360951642397207568q^{46} \) \(\mathstrut +\mathstrut 3175896146954973456q^{47} \) \(\mathstrut +\mathstrut 16109794963357781328q^{48} \) \(\mathstrut +\mathstrut 47566588174835497947q^{49} \) \(\mathstrut -\mathstrut 47980039081973985150q^{50} \) \(\mathstrut +\mathstrut 36297207934472600154q^{51} \) \(\mathstrut +\mathstrut 9189313650340970136q^{52} \) \(\mathstrut -\mathstrut 85640133844691747478q^{53} \) \(\mathstrut +\mathstrut 13174973542736589510q^{54} \) \(\mathstrut +\mathstrut 116776938927708191880q^{55} \) \(\mathstrut -\mathstrut 347340524381882787840q^{56} \) \(\mathstrut +\mathstrut 281201009602693342140q^{57} \) \(\mathstrut +\mathstrut 14348326854495898980q^{58} \) \(\mathstrut -\mathstrut 631511540910285077172q^{59} \) \(\mathstrut +\mathstrut 166566769635444959160q^{60} \) \(\mathstrut +\mathstrut 395554975976904438498q^{61} \) \(\mathstrut +\mathstrut 308631501962524143312q^{62} \) \(\mathstrut -\mathstrut 60742829120818879656q^{63} \) \(\mathstrut +\mathstrut 709112999898219261504q^{64} \) \(\mathstrut +\mathstrut 935439382588862006940q^{65} \) \(\mathstrut -\mathstrut 353613077321634457272q^{66} \) \(\mathstrut -\mathstrut 2276618325848154423084q^{67} \) \(\mathstrut +\mathstrut 903863999237509645128q^{68} \) \(\mathstrut -\mathstrut 1789447351552410715704q^{69} \) \(\mathstrut -\mathstrut 2140000160329520565120q^{70} \) \(\mathstrut +\mathstrut 3167518953231611655336q^{71} \) \(\mathstrut -\mathstrut 468129513645994441320q^{72} \) \(\mathstrut +\mathstrut 540985548741739085742q^{73} \) \(\mathstrut +\mathstrut 3755557695246314321796q^{74} \) \(\mathstrut -\mathstrut 4312425938123222362125q^{75} \) \(\mathstrut -\mathstrut 3600932441275465240368q^{76} \) \(\mathstrut +\mathstrut 7031798654764601316192q^{77} \) \(\mathstrut -\mathstrut 2689574919341493363804q^{78} \) \(\mathstrut -\mathstrut 6851064706666495753440q^{79} \) \(\mathstrut +\mathstrut 10282179571218820836960q^{80} \) \(\mathstrut +\mathstrut 2954312706550833698643q^{81} \) \(\mathstrut +\mathstrut 19297610262001226777292q^{82} \) \(\mathstrut -\mathstrut 15987031797819817516668q^{83} \) \(\mathstrut +\mathstrut 9703154081397258837504q^{84} \) \(\mathstrut -\mathstrut 3872123027340858752940q^{85} \) \(\mathstrut -\mathstrut 45738591650511680689176q^{86} \) \(\mathstrut +\mathstrut 17115135220034459638110q^{87} \) \(\mathstrut +\mathstrut 12797059799931801783840q^{88} \) \(\mathstrut -\mathstrut 66907017892222362195138q^{89} \) \(\mathstrut +\mathstrut 17973549048628266828660q^{90} \) \(\mathstrut +\mathstrut 58317327689277493187472q^{91} \) \(\mathstrut -\mathstrut 31420113320331180740064q^{92} \) \(\mathstrut +\mathstrut 32234358655239164369136q^{93} \) \(\mathstrut -\mathstrut 48807338646663610328448q^{94} \) \(\mathstrut +\mathstrut 73460040367269786796920q^{95} \) \(\mathstrut +\mathstrut 1002798900280998233568q^{96} \) \(\mathstrut +\mathstrut 76532691481778702340006q^{97} \) \(\mathstrut -\mathstrut 79581784673456500376322q^{98} \) \(\mathstrut +\mathstrut 1277497403922573971676q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.24.a.a \(1\) \(10.056\) \(\Q\) None \(1128\) \(177147\) \(-48863730\) \(-1723688680\) \(-\) \(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b \(2\) \(10.056\) \(\Q(\sqrt{530401}) \) None \(-1242\) \(-354294\) \(-46808820\) \(-211963904\) \(+\) \(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)