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Properties

Label 1008.4.do
Level $1008$
Weight $4$
Character orbit 1008.do
Rep. character $\chi_{1008}(205,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2288$
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.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1008 \)
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 2320 2320 0
Cusp forms 2288 2288 0
Eisenstein series 32 32 0

Trace form

\( 2288 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{6} - 16 q^{8} + O(q^{10}) \) \( 2288 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 4 q^{10} - 4 q^{11} - 2 q^{12} - 4 q^{13} - 34 q^{14} - 16 q^{15} + 2 q^{16} - 8 q^{17} - 174 q^{18} - 4 q^{19} - 4 q^{20} + 104 q^{21} - 4 q^{22} + 498 q^{24} - 4 q^{26} - 8 q^{27} + 120 q^{28} - 4 q^{29} + 1190 q^{30} + 4 q^{31} + 982 q^{32} - 4 q^{33} + 12 q^{34} + 242 q^{35} - 100 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{40} + 14 q^{42} - 4 q^{43} - 774 q^{44} + 998 q^{45} + 28 q^{46} + 3764 q^{47} - 48 q^{48} - 4 q^{49} + 28 q^{50} + 1506 q^{51} - 4 q^{52} - 4 q^{53} - 1046 q^{54} - 1316 q^{56} - 4 q^{58} + 2 q^{59} - 1946 q^{60} + 2 q^{61} - 1720 q^{62} - 1380 q^{63} - 16 q^{64} + 4 q^{65} - 2170 q^{66} + 2 q^{67} + 508 q^{68} + 46 q^{69} + 684 q^{70} + 3010 q^{72} + 3636 q^{74} - 36 q^{75} - 4 q^{76} + 2742 q^{77} + 2934 q^{78} + 4 q^{79} - 4 q^{80} - 4 q^{81} - 20 q^{82} + 1216 q^{83} + 1844 q^{84} + 246 q^{85} - 5564 q^{86} - 4 q^{88} - 584 q^{90} - 1380 q^{91} + 252 q^{92} + 106 q^{93} + 66 q^{94} + 4 q^{95} + 6612 q^{96} - 8 q^{97} + 3002 q^{98} + 1450 q^{99} + O(q^{100}) \)

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.