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Properties

Label 2394.4.k
Level $2394$
Weight $4$
Character orbit 2394.k
Rep. character $\chi_{2394}(799,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $648$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 2896 648 2248
Cusp forms 2864 648 2216
Eisenstein series 32 0 32

Trace form

\( 648 q + 16 q^{3} - 1296 q^{4} + 32 q^{5} - 256 q^{9} + O(q^{10}) \) \( 648 q + 16 q^{3} - 1296 q^{4} + 32 q^{5} - 256 q^{9} + 72 q^{11} + 64 q^{12} + 456 q^{15} - 5184 q^{16} + 128 q^{20} - 224 q^{21} - 928 q^{23} - 8676 q^{25} + 592 q^{27} - 832 q^{29} - 144 q^{31} + 1408 q^{33} - 560 q^{35} + 1280 q^{36} - 576 q^{37} - 1024 q^{39} - 576 q^{44} - 664 q^{45} + 776 q^{47} - 512 q^{48} - 15876 q^{49} - 1048 q^{51} + 272 q^{53} - 3168 q^{55} + 1328 q^{59} - 1440 q^{60} + 41472 q^{64} + 1280 q^{65} + 2448 q^{67} + 2472 q^{69} + 3792 q^{71} + 2960 q^{74} - 4320 q^{75} + 1232 q^{77} + 112 q^{78} - 1872 q^{79} - 1024 q^{80} + 3088 q^{81} - 7488 q^{82} - 3064 q^{83} + 1792 q^{84} + 1872 q^{85} - 800 q^{86} + 4432 q^{87} + 5120 q^{89} - 2080 q^{90} + 2016 q^{91} - 3712 q^{92} - 4768 q^{93} + 6192 q^{97} + 4136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)