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Properties

Label 3744.2.ix
Level $3744$
Weight $2$
Character orbit 3744.ix
Rep. character $\chi_{3744}(187,\cdot)$
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.ix (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

\( 5344 q - 4 q^{2} - 16 q^{3} - 4 q^{5} + 4 q^{6} - 8 q^{7} - 16 q^{8} - 16 q^{9} + O(q^{10}) \) \( 5344 q - 4 q^{2} - 16 q^{3} - 4 q^{5} + 4 q^{6} - 8 q^{7} - 16 q^{8} - 16 q^{9} - 4 q^{11} + 48 q^{12} - 4 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 40 q^{24} - 16 q^{26} - 16 q^{27} + 16 q^{28} - 8 q^{29} - 4 q^{32} - 16 q^{33} - 12 q^{34} - 32 q^{35} - 16 q^{37} - 32 q^{39} - 8 q^{40} + 24 q^{42} - 16 q^{44} - 28 q^{45} - 8 q^{47} - 16 q^{48} - 2576 q^{49} + 64 q^{50} - 4 q^{52} - 32 q^{53} - 8 q^{54} - 32 q^{55} - 56 q^{56} - 16 q^{57} + 32 q^{58} - 28 q^{59} - 24 q^{60} - 8 q^{61} + 56 q^{63} - 8 q^{65} - 16 q^{66} - 4 q^{67} - 40 q^{68} - 32 q^{70} + 40 q^{72} - 32 q^{73} - 8 q^{74} - 4 q^{76} + 112 q^{77} - 32 q^{78} - 16 q^{79} - 80 q^{80} - 176 q^{82} - 4 q^{83} + 172 q^{84} - 24 q^{85} - 108 q^{86} - 16 q^{87} + 48 q^{88} + 40 q^{91} - 8 q^{92} - 68 q^{93} - 8 q^{94} - 120 q^{96} - 8 q^{97} + 56 q^{98} + 92 q^{99} + O(q^{100}) \)

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.