↑

Properties

Label 3344.2.ej
Level $3344$
Weight $2$
Character orbit 3344.ej
Rep. character $\chi_{3344}(293,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $7616$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.ej (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3344 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616 q - 30 q^{2} - 18 q^{3} - 6 q^{4} - 6 q^{5} - 10 q^{6} + O(q^{10}) \) \( 7616 q - 30 q^{2} - 18 q^{3} - 6 q^{4} - 6 q^{5} - 10 q^{6} - 32 q^{11} - 30 q^{13} + 6 q^{14} - 36 q^{15} - 6 q^{16} - 20 q^{17} - 20 q^{19} - 24 q^{20} - 24 q^{22} - 10 q^{24} - 20 q^{26} - 10 q^{28} - 30 q^{29} - 40 q^{30} - 48 q^{33} - 108 q^{34} - 10 q^{35} + 26 q^{36} - 68 q^{38} - 30 q^{40} - 2 q^{42} - 58 q^{44} - 12 q^{47} - 18 q^{48} - 1856 q^{49} - 30 q^{51} - 30 q^{52} - 18 q^{53} - 24 q^{58} - 18 q^{59} - 18 q^{60} - 10 q^{61} - 10 q^{62} - 20 q^{63} - 168 q^{64} - 48 q^{66} - 48 q^{67} - 40 q^{68} - 72 q^{70} - 30 q^{72} + 90 q^{74} + 24 q^{77} + 264 q^{78} - 60 q^{79} + 22 q^{80} - 900 q^{81} - 90 q^{82} + 160 q^{83} - 10 q^{85} - 18 q^{86} - 30 q^{90} + 66 q^{91} - 54 q^{92} - 18 q^{93} - 40 q^{95} - 240 q^{96} - 36 q^{97} + 18 q^{99} + O(q^{100}) \)

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.