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Properties

Label 1008.3.el
Level $1008$
Weight $3$
Character orbit 1008.el
Rep. character $\chi_{1008}(221,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1520$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.el (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1008 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 1552 1552 0
Cusp forms 1520 1520 0
Eisenstein series 32 32 0

Trace form

\( 1520 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 8 q^{6} + O(q^{10}) \) \( 1520 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 8 q^{6} - 4 q^{10} - 2 q^{12} - 4 q^{13} - 6 q^{14} - 16 q^{15} + 2 q^{16} + 114 q^{18} - 4 q^{19} - 12 q^{20} + 32 q^{21} - 4 q^{22} + 138 q^{24} - 8 q^{27} + 24 q^{28} - 12 q^{29} - 58 q^{30} + 4 q^{31} - 6 q^{32} - 4 q^{33} - 12 q^{34} - 150 q^{35} - 76 q^{36} - 4 q^{37} - 4 q^{40} - 286 q^{42} - 4 q^{43} + 198 q^{44} - 202 q^{45} - 20 q^{46} - 12 q^{47} - 288 q^{48} - 4 q^{49} - 12 q^{50} - 198 q^{51} - 4 q^{52} - 590 q^{54} - 300 q^{56} - 4 q^{58} - 6 q^{59} + 142 q^{60} + 2 q^{61} - 204 q^{63} - 16 q^{64} - 12 q^{65} + 422 q^{66} + 2 q^{67} - 26 q^{69} + 96 q^{70} - 158 q^{72} + 120 q^{75} - 4 q^{76} - 6 q^{77} - 54 q^{78} + 4 q^{79} - 4 q^{81} + 4 q^{82} + 708 q^{83} - 28 q^{84} - 54 q^{85} - 4 q^{88} - 152 q^{90} - 204 q^{91} - 12 q^{92} + 34 q^{93} - 30 q^{94} - 12 q^{95} - 540 q^{96} - 8 q^{97} - 330 q^{98} - 170 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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