Properties

Label 3.12
Level 3
Weight 12
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(3))\).

Total New Old
Modular forms 5 1 4
Cusp forms 3 1 2
Eisenstein series 2 0 2

Trace form

\( q + 78q^{2} - 243q^{3} + 4036q^{4} - 5370q^{5} - 18954q^{6} - 27760q^{7} + 155064q^{8} + 59049q^{9} + O(q^{10}) \) \( q + 78q^{2} - 243q^{3} + 4036q^{4} - 5370q^{5} - 18954q^{6} - 27760q^{7} + 155064q^{8} + 59049q^{9} - 418860q^{10} + 637836q^{11} - 980748q^{12} + 766214q^{13} - 2165280q^{14} + 1304910q^{15} + 3829264q^{16} + 3084354q^{17} + 4605822q^{18} - 19511404q^{19} - 21673320q^{20} + 6745680q^{21} + 49751208q^{22} + 15312360q^{23} - 37680552q^{24} - 19991225q^{25} + 59764692q^{26} - 14348907q^{27} - 112039360q^{28} + 10751262q^{29} + 101782980q^{30} - 50937400q^{31} - 18888480q^{32} - 154994148q^{33} + 240579612q^{34} + 149071200q^{35} + 238321764q^{36} + 664740830q^{37} - 1521889512q^{38} - 186190002q^{39} - 832693680q^{40} + 898833450q^{41} + 526163040q^{42} - 957947188q^{43} + 2574306096q^{44} - 317093130q^{45} + 1194364080q^{46} - 1555741344q^{47} - 930511152q^{48} - 1206709143q^{49} - 1559315550q^{50} - 749498022q^{51} + 3092439704q^{52} + 3792417030q^{53} - 1119214746q^{54} - 3425179320q^{55} - 4304576640q^{56} + 4741271172q^{57} + 838598436q^{58} + 555306924q^{59} + 5266616760q^{60} + 4950420998q^{61} - 3973117200q^{62} - 1639200240q^{63} - 9315634112q^{64} - 4114569180q^{65} - 12089543544q^{66} + 5292399284q^{67} + 12448452744q^{68} - 3720903480q^{69} + 11627553600q^{70} - 14831086248q^{71} + 9156374136q^{72} + 13971005210q^{73} + 51849784740q^{74} + 4857867675q^{75} - 78748026544q^{76} - 17706327360q^{77} - 14522820156q^{78} + 3720542360q^{79} - 20563147680q^{80} + 3486784401q^{81} + 70109009100q^{82} + 8768454036q^{83} + 27225564480q^{84} - 16562980980q^{85} - 74719880664q^{86} - 2612556666q^{87} + 98905401504q^{88} - 25472769174q^{89} - 24733264140q^{90} - 21270100640q^{91} + 61800684960q^{92} + 12377788200q^{93} - 121347824832q^{94} + 104776239480q^{95} + 4589900640q^{96} - 39092494846q^{97} - 94123313154q^{98} + 37663577964q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.12.a \(\chi_{3}(1, \cdot)\) 3.12.a.a 1 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)