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Properties

Label 2394.2.l
Level $2394$
Weight $2$
Character orbit 2394.l
Rep. character $\chi_{2394}(163,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $136$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
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 992 136 856
Cusp forms 928 136 792
Eisenstein series 64 0 64

Trace form

\( 136 q - 68 q^{4} + 2 q^{5} - 6 q^{7} + O(q^{10}) \) \( 136 q - 68 q^{4} + 2 q^{5} - 6 q^{7} - 4 q^{10} - 6 q^{13} + 10 q^{14} - 68 q^{16} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 4 q^{23} - 74 q^{25} + 4 q^{26} + 2 q^{29} - 10 q^{31} - 4 q^{34} + 2 q^{35} - 22 q^{37} - 12 q^{38} - 4 q^{40} + 14 q^{41} - 20 q^{43} + 6 q^{46} + 8 q^{47} - 10 q^{49} + 48 q^{50} + 12 q^{52} - 18 q^{53} - 2 q^{55} - 8 q^{56} + 4 q^{58} - 20 q^{59} + 8 q^{61} + 4 q^{62} + 136 q^{64} + 12 q^{65} - 8 q^{67} - 4 q^{70} - 2 q^{71} - 4 q^{73} + 8 q^{74} - 12 q^{76} - 10 q^{77} + 14 q^{79} + 2 q^{80} - 32 q^{82} - 8 q^{83} + 24 q^{85} - 8 q^{86} - 6 q^{88} - 112 q^{89} + 24 q^{91} + 2 q^{92} - 6 q^{94} + 66 q^{95} - 22 q^{97} + 4 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)