Properties

Label 3.24.a
Level $3$
Weight $24$
Character orbit 3.a
Rep. character $\chi_{3}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces

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

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