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Properties

Label 2394.2.i
Level $2394$
Weight $2$
Character orbit 2394.i
Rep. character $\chi_{2394}(1255,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $288$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 976 288 688
Cusp forms 944 288 656
Eisenstein series 32 0 32

Trace form

\( 288 q + 288 q^{4} + 8 q^{5} + 8 q^{6} + 16 q^{9} + O(q^{10}) \) \( 288 q + 288 q^{4} + 8 q^{5} + 8 q^{6} + 16 q^{9} - 8 q^{11} - 4 q^{14} + 8 q^{15} + 288 q^{16} + 16 q^{17} + 16 q^{18} + 8 q^{20} + 28 q^{21} + 12 q^{23} + 8 q^{24} - 144 q^{25} + 32 q^{26} - 24 q^{27} + 20 q^{29} - 16 q^{30} + 80 q^{33} + 4 q^{35} + 16 q^{36} + 12 q^{38} - 10 q^{39} - 20 q^{41} + 2 q^{42} - 8 q^{44} - 84 q^{45} + 12 q^{46} - 12 q^{47} - 12 q^{49} + 4 q^{51} - 32 q^{53} - 22 q^{54} + 24 q^{55} - 4 q^{56} - 12 q^{58} + 8 q^{60} - 24 q^{61} - 88 q^{62} - 50 q^{63} + 288 q^{64} - 40 q^{65} + 16 q^{68} + 4 q^{69} + 36 q^{70} - 16 q^{71} + 16 q^{72} + 6 q^{74} - 108 q^{75} - 20 q^{77} - 48 q^{78} + 72 q^{79} + 8 q^{80} + 48 q^{81} - 32 q^{83} + 28 q^{84} - 24 q^{85} - 24 q^{86} - 16 q^{87} + 24 q^{89} - 12 q^{90} + 12 q^{92} + 52 q^{93} + 48 q^{94} + 8 q^{96} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \)