Properties

Label 2394.4.dl
Level $2394$
Weight $4$
Character orbit 2394.dl
Rep. character $\chi_{2394}(113,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $720$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.dl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2394, [\chi])\).

Total New Old
Modular forms 2896 720 2176
Cusp forms 2864 720 2144
Eisenstein series 32 0 32

Trace form

\( 720 q - 1440 q^{4} - 40 q^{6} - 20 q^{9} + O(q^{10}) \) \( 720 q - 1440 q^{4} - 40 q^{6} - 20 q^{9} + 300 q^{11} - 5760 q^{16} + 180 q^{19} + 312 q^{23} - 160 q^{24} + 9000 q^{25} + 896 q^{30} - 80 q^{36} + 564 q^{38} + 968 q^{39} + 684 q^{43} + 3792 q^{45} + 4560 q^{47} - 17640 q^{49} + 2072 q^{54} - 1310 q^{57} - 1288 q^{63} + 46080 q^{64} - 2800 q^{66} + 912 q^{68} + 1656 q^{73} + 3648 q^{74} - 360 q^{76} - 5668 q^{81} - 4176 q^{82} - 6672 q^{83} - 10912 q^{87} - 1248 q^{92} + 5128 q^{93} + 13908 q^{95} + 1280 q^{96} - 3656 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

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