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Properties

Label 2394.4.gh
Level $2394$
Weight $4$
Character orbit 2394.gh
Rep. character $\chi_{2394}(155,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2160$
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.gh (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 8688 2160 6528
Cusp forms 8592 2160 6432
Eisenstein series 96 0 96

Trace form

\( 2160 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + O(q^{10}) \) \( 2160 q - 6 q^{3} - 60 q^{6} - 30 q^{9} + 132 q^{15} + 72 q^{18} - 108 q^{22} + 480 q^{24} + 1314 q^{27} - 2160 q^{29} - 78 q^{33} - 120 q^{36} - 1908 q^{38} - 1824 q^{39} + 90 q^{41} + 684 q^{45} + 96 q^{48} + 105840 q^{49} - 4500 q^{51} - 3456 q^{54} + 4128 q^{57} - 2898 q^{59} - 528 q^{60} - 336 q^{63} - 69120 q^{64} + 6120 q^{66} + 2322 q^{67} + 10800 q^{69} + 1104 q^{72} + 2484 q^{73} + 5064 q^{78} - 1758 q^{81} + 3132 q^{82} + 5952 q^{87} - 5940 q^{89} + 3960 q^{90} + 1872 q^{92} - 7320 q^{93} + 54 q^{97} + 7626 q^{99} + O(q^{100}) \)

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

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