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Properties

Label 3344.2.fi
Level $3344$
Weight $2$
Character orbit 3344.fi
Rep. character $\chi_{3344}(5,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $22848$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.fi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3344 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3344, [\chi])\).

Total New Old
Modular forms 23232 23232 0
Cusp forms 22848 22848 0
Eisenstein series 384 384 0

Trace form

\( 22848 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{5} - 36 q^{6} - 18 q^{8} + O(q^{10}) \) \( 22848 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{5} - 36 q^{6} - 18 q^{8} - 96 q^{10} - 24 q^{11} - 48 q^{12} - 36 q^{13} - 12 q^{14} - 72 q^{15} - 36 q^{16} - 72 q^{17} - 72 q^{18} - 36 q^{19} - 72 q^{20} - 60 q^{21} - 48 q^{22} - 36 q^{24} + 78 q^{26} - 18 q^{27} + 12 q^{28} - 36 q^{29} - 18 q^{30} - 36 q^{31} - 36 q^{32} - 96 q^{33} + 24 q^{34} + 24 q^{35} - 36 q^{36} - 72 q^{37} - 204 q^{38} - 96 q^{40} + 156 q^{42} - 96 q^{43} - 114 q^{44} - 48 q^{45} - 18 q^{46} - 72 q^{47} - 36 q^{48} - 2748 q^{49} - 18 q^{50} - 36 q^{51} - 132 q^{52} - 36 q^{53} - 228 q^{54} - 24 q^{56} - 72 q^{58} - 36 q^{59} - 36 q^{60} - 36 q^{61} - 60 q^{62} + 96 q^{63} - 18 q^{64} - 96 q^{65} - 48 q^{66} - 96 q^{67} - 18 q^{68} - 18 q^{69} - 234 q^{70} + 60 q^{72} - 36 q^{74} - 72 q^{75} - 480 q^{76} - 12 q^{77} - 432 q^{78} - 72 q^{79} - 96 q^{80} - 72 q^{81} - 96 q^{82} - 18 q^{83} - 270 q^{84} - 36 q^{85} - 36 q^{86} - 24 q^{88} - 36 q^{90} + 48 q^{91} - 36 q^{92} - 72 q^{93} + 180 q^{94} - 72 q^{95} + 120 q^{96} - 72 q^{97} - 36 q^{98} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3344, [\chi])\) into newform subspaces

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