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Properties

Label 1008.4.du
Level $1008$
Weight $4$
Character orbit 1008.du
Rep. character $\chi_{1008}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $952$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.du (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 2336 968 1368
Cusp forms 2272 952 1320
Eisenstein series 64 16 48

Trace form

\( 952 q + 2 q^{2} - 12 q^{4} + 2 q^{5} + 92 q^{8} + O(q^{10}) \) \( 952 q + 2 q^{2} - 12 q^{4} + 2 q^{5} + 92 q^{8} - 8 q^{10} - 18 q^{11} - 8 q^{13} + 228 q^{14} - 32 q^{16} + 4 q^{17} - 2 q^{19} + 88 q^{20} - 748 q^{22} + 2 q^{26} - 358 q^{28} - 392 q^{29} - 748 q^{31} - 488 q^{32} - 264 q^{34} + 26 q^{35} + 6 q^{37} + 222 q^{38} + 490 q^{40} - 816 q^{43} + 98 q^{44} + 316 q^{46} - 1876 q^{47} - 8 q^{49} + 768 q^{50} + 52 q^{52} + 378 q^{53} - 3408 q^{56} + 98 q^{58} + 690 q^{59} - 2 q^{61} - 124 q^{62} + 5424 q^{64} + 4 q^{65} + 718 q^{67} + 756 q^{68} + 1160 q^{70} - 82 q^{74} + 604 q^{76} + 690 q^{77} - 4 q^{79} + 112 q^{80} + 1754 q^{82} - 2432 q^{83} + 492 q^{85} + 6956 q^{86} - 250 q^{88} + 2320 q^{91} - 2060 q^{92} + 210 q^{94} + 3868 q^{95} - 16 q^{97} + 3412 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)