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Properties

Label 2394.4.er
Level $2394$
Weight $4$
Character orbit 2394.er
Rep. character $\chi_{2394}(29,\cdot)$
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.er (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

\( 2160 q + 12 q^{3} + 120 q^{6} + 60 q^{9} + O(q^{10}) \) \( 2160 q + 12 q^{3} + 120 q^{6} + 60 q^{9} + 132 q^{15} - 72 q^{18} - 108 q^{22} - 468 q^{23} - 240 q^{24} + 1314 q^{27} + 1992 q^{33} + 240 q^{36} - 1824 q^{39} + 684 q^{45} + 96 q^{48} - 52920 q^{49} - 4500 q^{51} - 3456 q^{54} - 1344 q^{57} - 528 q^{60} - 336 q^{63} - 69120 q^{64} - 3060 q^{66} - 4644 q^{67} + 1368 q^{68} + 1104 q^{72} + 2484 q^{73} + 2688 q^{78} - 6708 q^{81} + 3132 q^{82} - 10656 q^{83} - 2976 q^{87} + 5940 q^{89} + 3960 q^{90} + 10284 q^{93} - 108 q^{97} + 7626 q^{99} + O(q^{100}) \)

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

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