↑

Properties

Label 3744.2.in
Level $3744$
Weight $2$
Character orbit 3744.in
Rep. character $\chi_{3744}(317,\cdot)$
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.in (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

\( 5344 q - 12 q^{2} - 16 q^{3} - 12 q^{5} + 4 q^{6} - 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 5344 q - 12 q^{2} - 16 q^{3} - 12 q^{5} + 4 q^{6} - 8 q^{7} - 16 q^{9} - 12 q^{11} + 48 q^{12} - 4 q^{13} - 24 q^{14} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{22} + 24 q^{24} - 16 q^{27} + 16 q^{28} - 24 q^{29} - 8 q^{31} - 12 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{37} + 16 q^{39} - 8 q^{40} - 24 q^{41} + 24 q^{42} - 28 q^{45} - 32 q^{46} - 16 q^{48} - 2576 q^{49} - 168 q^{50} - 4 q^{52} - 8 q^{54} - 32 q^{55} + 168 q^{56} - 40 q^{58} - 84 q^{59} + 8 q^{60} - 8 q^{61} - 16 q^{63} - 24 q^{65} - 16 q^{66} - 4 q^{67} + 72 q^{68} - 32 q^{70} - 184 q^{72} - 24 q^{74} - 4 q^{76} + 40 q^{78} + 112 q^{82} - 12 q^{83} - 132 q^{84} + 16 q^{85} - 12 q^{86} - 16 q^{87} + 48 q^{88} + 40 q^{91} - 24 q^{92} + 52 q^{93} - 8 q^{94} - 184 q^{96} - 8 q^{97} + 92 q^{99} + O(q^{100}) \)

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.