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Properties

Label 2394.4.u
Level $2394$
Weight $4$
Character orbit 2394.u
Rep. character $\chi_{2394}(457,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $864$
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.u (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 864 2032
Cusp forms 2864 864 2000
Eisenstein series 32 0 32

Trace form

\( 864 q - 1728 q^{4} + 80 q^{5} - 16 q^{6} - 92 q^{9} + O(q^{10}) \) \( 864 q - 1728 q^{4} + 80 q^{5} - 16 q^{6} - 92 q^{9} - 32 q^{11} - 88 q^{14} + 80 q^{15} - 6912 q^{16} - 272 q^{17} + 112 q^{18} - 160 q^{20} + 28 q^{21} + 336 q^{23} + 32 q^{24} + 21600 q^{25} - 544 q^{26} + 300 q^{27} + 860 q^{29} + 728 q^{30} + 776 q^{33} + 544 q^{35} - 32 q^{36} + 912 q^{38} - 1636 q^{39} - 548 q^{41} + 1040 q^{42} + 64 q^{44} - 60 q^{45} - 504 q^{46} - 66 q^{47} - 792 q^{49} - 3212 q^{51} - 392 q^{53} + 1076 q^{54} - 1224 q^{55} + 704 q^{56} - 1008 q^{58} - 640 q^{60} + 36 q^{61} + 2000 q^{62} + 1702 q^{63} + 55296 q^{64} - 2848 q^{65} + 2880 q^{66} + 2176 q^{68} + 2704 q^{69} - 432 q^{70} + 2288 q^{71} + 448 q^{72} - 840 q^{74} - 432 q^{75} - 1448 q^{77} + 2592 q^{78} + 1620 q^{79} - 640 q^{80} + 2652 q^{81} - 1880 q^{83} + 112 q^{84} + 1440 q^{85} + 2208 q^{86} + 2576 q^{87} + 2508 q^{89} - 1992 q^{90} - 672 q^{92} + 4960 q^{93} - 2448 q^{94} + 128 q^{96} + 2880 q^{98} - 3776 q^{99} + O(q^{100}) \)

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

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