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Properties

Label 2394.4.n
Level $2394$
Weight $4$
Character orbit 2394.n
Rep. character $\chi_{2394}(2059,\cdot)$
Character field $\Q(\zeta_{3})$
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.n (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 720 2176
Cusp forms 2864 720 2144
Eisenstein series 32 0 32

Trace form

\( 720 q + 16 q^{2} + 4 q^{3} + 2880 q^{4} + 40 q^{6} + 64 q^{8} - 20 q^{9} + O(q^{10}) \) \( 720 q + 16 q^{2} + 4 q^{3} + 2880 q^{4} + 40 q^{6} + 64 q^{8} - 20 q^{9} + 50 q^{11} + 16 q^{12} - 112 q^{14} + 44 q^{15} + 11520 q^{16} - 76 q^{17} + 168 q^{18} + 90 q^{19} - 36 q^{22} - 104 q^{23} + 160 q^{24} - 9000 q^{25} - 1208 q^{27} - 936 q^{29} + 176 q^{30} + 256 q^{32} + 452 q^{33} - 360 q^{34} - 80 q^{36} - 260 q^{38} - 1580 q^{39} + 1014 q^{41} + 1368 q^{43} + 200 q^{44} - 2352 q^{45} + 704 q^{47} + 64 q^{48} - 17640 q^{49} - 1024 q^{50} - 570 q^{51} - 1624 q^{53} + 2176 q^{54} - 448 q^{56} + 12 q^{57} - 1026 q^{59} + 176 q^{60} - 312 q^{62} + 840 q^{63} + 46080 q^{64} + 32 q^{65} + 1696 q^{66} - 1548 q^{67} - 304 q^{68} + 4972 q^{69} - 160 q^{71} + 672 q^{72} - 414 q^{73} - 2432 q^{74} - 1270 q^{75} + 360 q^{76} + 2648 q^{78} + 2100 q^{81} + 1044 q^{82} + 1924 q^{83} + 10128 q^{86} - 5952 q^{87} - 144 q^{88} + 2540 q^{89} - 3120 q^{90} - 416 q^{92} + 8008 q^{93} - 1820 q^{95} + 640 q^{96} - 36 q^{97} - 392 q^{98} + 5146 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2394, [\chi]) \cong \)