Properties

Label 1008.3.dw
Level $1008$
Weight $3$
Character orbit 1008.dw
Rep. character $\chi_{1008}(131,\cdot)$
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.dw (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

\( 1520 q - 6 q^{3} - 4 q^{4} - 6 q^{5} - 4 q^{7} + O(q^{10}) \) \( 1520 q - 6 q^{3} - 4 q^{4} - 6 q^{5} - 4 q^{7} - 12 q^{10} - 6 q^{11} - 6 q^{12} - 6 q^{14} - 4 q^{16} + 16 q^{18} - 12 q^{19} - 22 q^{21} - 4 q^{22} - 12 q^{23} - 6 q^{24} - 40 q^{28} - 12 q^{29} - 30 q^{30} - 12 q^{33} + 24 q^{34} + 150 q^{35} + 124 q^{36} - 4 q^{37} - 6 q^{38} - 4 q^{39} - 6 q^{40} + 14 q^{42} - 4 q^{43} + 198 q^{44} - 6 q^{45} + 12 q^{46} - 4 q^{49} - 12 q^{50} - 46 q^{51} - 6 q^{52} + 78 q^{54} + 288 q^{56} + 2 q^{58} - 12 q^{59} + 90 q^{60} - 48 q^{62} - 16 q^{64} + 654 q^{66} - 4 q^{67} - 6 q^{68} - 54 q^{69} - 198 q^{70} - 158 q^{72} + 246 q^{74} - 6 q^{75} - 6 q^{77} - 38 q^{78} - 4 q^{81} - 36 q^{82} - 720 q^{83} - 806 q^{84} + 46 q^{85} - 906 q^{86} - 12 q^{87} + 2 q^{88} + 540 q^{90} - 204 q^{91} - 12 q^{92} - 74 q^{93} - 6 q^{96} - 282 q^{98} - 170 q^{99} + O(q^{100}) \)

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

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