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Properties

Label 3744.2.jg
Level $3744$
Weight $2$
Character orbit 3744.jg
Rep. character $\chi_{3744}(563,\cdot)$
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.jg (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

\( 5344 q - 24 q^{2} - 4 q^{3} - 8 q^{4} - 12 q^{6} - 12 q^{7} - 4 q^{9} + O(q^{10}) \) \( 5344 q - 24 q^{2} - 4 q^{3} - 8 q^{4} - 12 q^{6} - 12 q^{7} - 4 q^{9} - 8 q^{10} - 24 q^{11} - 16 q^{12} - 4 q^{13} - 24 q^{14} - 24 q^{15} - 8 q^{16} - 24 q^{19} - 12 q^{20} - 8 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} + 8 q^{27} - 24 q^{28} - 36 q^{30} - 24 q^{32} - 24 q^{33} + 24 q^{34} + 8 q^{36} - 24 q^{37} - 24 q^{38} - 32 q^{39} - 8 q^{40} - 12 q^{41} - 44 q^{42} + 4 q^{43} - 12 q^{45} - 24 q^{46} + 100 q^{48} - 12 q^{50} + 8 q^{51} - 4 q^{52} - 12 q^{54} - 8 q^{55} - 12 q^{56} - 24 q^{59} - 48 q^{60} + 4 q^{61} - 12 q^{62} - 32 q^{64} - 24 q^{65} + 104 q^{66} - 12 q^{67} + 84 q^{68} - 4 q^{69} - 12 q^{72} - 12 q^{74} + 36 q^{75} - 12 q^{76} - 24 q^{77} + 44 q^{78} - 16 q^{79} - 8 q^{82} - 12 q^{84} - 4 q^{87} - 8 q^{88} + 56 q^{90} - 16 q^{91} - 24 q^{92} - 12 q^{93} - 12 q^{94} + 96 q^{96} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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