↑

Properties

Label 3744.2.kl
Level $3744$
Weight $2$
Character orbit 3744.kl
Rep. character $\chi_{3744}(149,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $5344$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.kl (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

\( 5344 q - 12 q^{2} - 4 q^{3} - 12 q^{5} - 20 q^{6} - 12 q^{7} - 4 q^{9} + O(q^{10}) \) \( 5344 q - 12 q^{2} - 4 q^{3} - 12 q^{5} - 20 q^{6} - 12 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{11} + 24 q^{12} - 4 q^{13} - 24 q^{14} - 8 q^{16} - 24 q^{18} - 16 q^{19} - 12 q^{20} - 20 q^{21} - 8 q^{22} - 12 q^{23} - 40 q^{24} - 16 q^{27} - 12 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{33} - 20 q^{34} - 60 q^{35} + 24 q^{36} - 16 q^{37} - 32 q^{39} - 8 q^{40} - 12 q^{41} + 36 q^{42} - 12 q^{43} + 12 q^{45} - 24 q^{46} - 4 q^{48} + 2576 q^{49} + 144 q^{50} - 4 q^{52} - 8 q^{54} - 8 q^{55} - 96 q^{56} - 16 q^{57} + 68 q^{58} - 12 q^{59} - 40 q^{60} + 4 q^{61} - 36 q^{62} - 16 q^{63} - 24 q^{65} - 16 q^{66} - 4 q^{67} + 48 q^{68} - 12 q^{69} - 60 q^{70} - 32 q^{73} - 12 q^{74} - 12 q^{75} - 4 q^{76} - 40 q^{78} - 96 q^{80} - 76 q^{82} - 12 q^{83} + 40 q^{84} + 16 q^{85} - 12 q^{86} - 4 q^{87} + 96 q^{88} + 12 q^{91} - 24 q^{92} + 100 q^{93} + 4 q^{94} - 48 q^{95} + 104 q^{96} - 8 q^{97} - 60 q^{98} + 128 q^{99} + O(q^{100}) \)

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.