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Properties

Label 2352.4.w
Level $2352$
Weight $4$
Character orbit 2352.w
Rep. character $\chi_{2352}(589,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $984$
Sturm bound $1792$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

Total New Old
Modular forms 2720 984 1736
Cusp forms 2656 984 1672
Eisenstein series 64 0 64

Trace form

\( 984 q + 20 q^{4} - 84 q^{8} + O(q^{10}) \) \( 984 q + 20 q^{4} - 84 q^{8} + 48 q^{10} + 40 q^{11} - 24 q^{12} + 120 q^{15} - 72 q^{16} + 36 q^{18} + 24 q^{19} - 80 q^{20} - 272 q^{22} + 228 q^{24} - 20 q^{26} - 400 q^{29} - 408 q^{30} + 744 q^{31} - 960 q^{32} - 992 q^{34} + 108 q^{36} - 16 q^{37} + 816 q^{38} - 104 q^{40} - 376 q^{43} + 1264 q^{44} - 32 q^{46} + 528 q^{48} - 3548 q^{50} + 744 q^{51} - 3744 q^{52} - 752 q^{53} + 108 q^{54} - 1936 q^{58} + 1376 q^{59} + 1224 q^{60} - 912 q^{61} - 1932 q^{62} + 56 q^{64} + 976 q^{65} + 1368 q^{66} + 2256 q^{67} + 2472 q^{68} - 528 q^{69} + 612 q^{72} - 1060 q^{74} + 1104 q^{75} - 3104 q^{76} - 1692 q^{78} + 5992 q^{79} - 7032 q^{80} - 79704 q^{81} - 3520 q^{82} + 2680 q^{83} - 240 q^{85} + 13624 q^{86} - 1712 q^{88} + 648 q^{90} + 4568 q^{92} - 1568 q^{94} + 7728 q^{95} - 2280 q^{96} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)