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Properties

Label 2394.2.s
Level $2394$
Weight $2$
Character orbit 2394.s
Rep. character $\chi_{2394}(463,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
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.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 976 240 736
Cusp forms 944 240 704
Eisenstein series 32 0 32

Trace form

\( 240 q + 4 q^{2} - 2 q^{3} - 120 q^{4} - 2 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{2} - 2 q^{3} - 120 q^{4} - 2 q^{6} - 8 q^{8} - 2 q^{9} + 2 q^{11} + 4 q^{12} - 16 q^{14} - 4 q^{15} - 120 q^{16} - 4 q^{17} + 12 q^{18} - 6 q^{19} - 12 q^{22} + 4 q^{23} - 2 q^{24} + 240 q^{25} + 16 q^{27} - 72 q^{29} - 16 q^{30} + 4 q^{32} + 50 q^{33} + 24 q^{34} - 2 q^{36} - 14 q^{38} + 16 q^{39} + 60 q^{41} - 12 q^{43} + 2 q^{44} - 24 q^{45} + 128 q^{47} - 2 q^{48} - 120 q^{49} + 32 q^{50} - 84 q^{51} + 32 q^{53} + 40 q^{54} + 8 q^{56} + 42 q^{57} + 36 q^{59} + 8 q^{60} + 12 q^{62} - 24 q^{63} + 240 q^{64} + 128 q^{65} + 10 q^{66} + 6 q^{67} - 4 q^{68} + 28 q^{69} - 16 q^{71} + 6 q^{72} + 6 q^{73} - 32 q^{74} - 34 q^{75} + 12 q^{76} - 64 q^{78} + 6 q^{81} + 6 q^{82} - 8 q^{83} + 12 q^{86} + 36 q^{87} + 6 q^{88} + 20 q^{89} - 36 q^{90} + 4 q^{92} + 52 q^{93} + 64 q^{95} + 4 q^{96} + 6 q^{97} + 4 q^{98} + 88 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)