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Properties

Label 3744.2.jv
Level $3744$
Weight $2$
Character orbit 3744.jv
Rep. character $\chi_{3744}(277,\cdot)$
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.jv (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

\( 5344 q - 12 q^{2} - 4 q^{3} + 4 q^{4} - 12 q^{6} - 4 q^{9} + O(q^{10}) \) \( 5344 q - 12 q^{2} - 4 q^{3} + 4 q^{4} - 12 q^{6} - 4 q^{9} - 8 q^{10} - 12 q^{11} - 16 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{16} - 24 q^{19} + 4 q^{22} - 8 q^{23} - 12 q^{24} - 8 q^{25} - 16 q^{26} - 40 q^{27} - 24 q^{28} + 4 q^{29} + 12 q^{30} - 12 q^{32} - 24 q^{33} + 24 q^{34} - 8 q^{35} - 28 q^{36} - 24 q^{37} - 8 q^{38} + 16 q^{39} - 8 q^{40} + 76 q^{42} - 8 q^{43} - 12 q^{45} - 24 q^{46} - 56 q^{48} - 40 q^{51} - 4 q^{52} - 32 q^{53} - 12 q^{54} - 8 q^{55} - 168 q^{56} - 12 q^{58} - 12 q^{59} - 48 q^{60} - 8 q^{61} - 28 q^{62} - 24 q^{63} - 32 q^{64} - 8 q^{65} - 136 q^{66} - 72 q^{68} - 4 q^{69} - 24 q^{71} - 12 q^{72} - 8 q^{74} - 24 q^{75} - 8 q^{77} - 72 q^{78} - 24 q^{80} - 8 q^{82} - 12 q^{84} - 72 q^{85} - 4 q^{87} + 4 q^{88} - 24 q^{89} + 56 q^{90} - 16 q^{91} - 8 q^{92} - 48 q^{93} + 24 q^{94} - 248 q^{95} + 96 q^{96} - 24 q^{98} + O(q^{100}) \)

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.