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Properties

Label 1008.4.dx
Level $1008$
Weight $4$
Character orbit 1008.dx
Rep. character $\chi_{1008}(277,\cdot)$
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.dx (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

\( 2288 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 8 q^{6} - 16 q^{8} + O(q^{10}) \) \( 2288 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 8 q^{6} - 16 q^{8} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 62 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{17} + 132 q^{18} - 4 q^{19} - 4 q^{20} - 58 q^{21} - 4 q^{22} + 498 q^{24} - 4 q^{26} - 8 q^{27} + 120 q^{28} - 4 q^{29} - 598 q^{30} - 8 q^{31} - 1964 q^{32} - 4 q^{33} + 12 q^{34} + 242 q^{35} - 100 q^{36} - 4 q^{37} + 2 q^{38} + 2 q^{40} + 1034 q^{42} - 4 q^{43} - 774 q^{44} - 502 q^{45} + 28 q^{46} - 7528 q^{47} - 48 q^{48} - 4 q^{49} + 28 q^{50} - 594 q^{51} + 2 q^{52} - 4 q^{53} - 1706 q^{54} + 1684 q^{56} + 2 q^{58} - 4 q^{59} + 610 q^{60} - 4 q^{61} - 1720 q^{62} + 2736 q^{63} - 16 q^{64} - 8 q^{65} + 1034 q^{66} - 4 q^{67} - 254 q^{68} + 46 q^{69} - 1374 q^{70} + 3010 q^{72} - 1818 q^{74} + 390 q^{75} - 4 q^{76} - 1374 q^{77} + 2934 q^{78} - 8 q^{79} - 4 q^{80} - 4 q^{81} - 20 q^{82} + 1216 q^{83} + 794 q^{84} + 246 q^{85} + 2782 q^{86} + 2 q^{88} - 584 q^{90} - 1380 q^{91} + 252 q^{92} - 218 q^{93} - 132 q^{94} - 8 q^{95} - 3078 q^{96} - 8 q^{97} + 3002 q^{98} + 1450 q^{99} + O(q^{100}) \)

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.