Properties

Label 2394.4.bh
Level $2394$
Weight $4$
Character orbit 2394.bh
Rep. character $\chi_{2394}(407,\cdot)$
Character field $\Q(\zeta_{6})$
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.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 720 q - 6 q^{3} - 1440 q^{4} + 20 q^{6} + 10 q^{9} + O(q^{10}) \) \( 720 q - 6 q^{3} - 1440 q^{4} + 20 q^{6} + 10 q^{9} - 150 q^{11} - 132 q^{15} - 5760 q^{16} - 228 q^{17} - 90 q^{19} + 156 q^{23} + 80 q^{24} - 18000 q^{25} + 1440 q^{29} - 448 q^{30} - 402 q^{33} + 40 q^{36} + 708 q^{38} + 1340 q^{39} - 60 q^{41} + 684 q^{43} + 600 q^{44} - 528 q^{45} + 96 q^{48} - 17640 q^{49} - 1128 q^{50} - 360 q^{51} + 1056 q^{53} + 416 q^{54} - 290 q^{57} + 1932 q^{59} + 936 q^{62} + 2240 q^{63} + 46080 q^{64} + 3192 q^{65} - 436 q^{66} + 2322 q^{67} + 912 q^{68} + 2724 q^{69} + 1104 q^{72} + 414 q^{73} - 3648 q^{74} - 1710 q^{75} + 720 q^{76} + 2928 q^{78} + 2978 q^{81} - 1044 q^{82} + 8664 q^{83} + 3968 q^{87} + 432 q^{88} - 1980 q^{89} + 4920 q^{90} - 624 q^{92} + 2908 q^{93} - 4128 q^{95} - 640 q^{96} + 54 q^{97} + 10024 q^{99} + O(q^{100}) \)

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

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