Properties

Label 3744.2.iq
Level $3744$
Weight $2$
Character orbit 3744.iq
Rep. character $\chi_{3744}(115,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $5344$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.iq (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3744 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

Total New Old
Modular forms 5408 5408 0
Cusp forms 5344 5344 0
Eisenstein series 64 64 0

Trace form

\( 5344 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 16 q^{8} - 4 q^{9} + O(q^{10}) \) \( 5344 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 16 q^{8} - 4 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 40 q^{14} - 16 q^{15} - 8 q^{16} + 8 q^{18} - 16 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 12 q^{23} - 40 q^{24} - 16 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 12 q^{30} - 4 q^{32} - 16 q^{33} + 12 q^{34} - 68 q^{35} + 24 q^{36} - 16 q^{37} - 32 q^{39} - 8 q^{40} - 12 q^{41} + 36 q^{42} - 12 q^{43} - 16 q^{44} - 28 q^{45} - 24 q^{46} - 8 q^{47} - 4 q^{48} - 2576 q^{49} + 16 q^{50} - 4 q^{52} - 32 q^{53} - 8 q^{54} - 8 q^{55} + 16 q^{56} - 16 q^{57} - 76 q^{58} + 44 q^{59} + 24 q^{60} + 4 q^{61} + 12 q^{62} + 56 q^{63} - 8 q^{65} - 16 q^{66} - 4 q^{67} + 128 q^{68} - 12 q^{69} + 52 q^{70} - 24 q^{71} - 128 q^{72} - 32 q^{73} + 4 q^{74} - 12 q^{75} - 4 q^{76} - 56 q^{77} + 112 q^{78} - 16 q^{79} + 16 q^{80} - 44 q^{82} - 4 q^{83} - 56 q^{84} - 24 q^{85} - 108 q^{86} - 4 q^{87} - 96 q^{88} - 24 q^{89} - 44 q^{91} - 8 q^{92} + 76 q^{93} + 4 q^{94} - 120 q^{96} - 8 q^{97} - 52 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.