Properties

Label 1008.2.dr
Level $1008$
Weight $2$
Character orbit 1008.dr
Rep. character $\chi_{1008}(5,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $752$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.dr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1008 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 784 784 0
Cusp forms 752 752 0
Eisenstein series 32 32 0

Trace form

\( 752 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + O(q^{10}) \) \( 752 q - 6 q^{3} - 4 q^{4} - 6 q^{5} - 12 q^{10} - 6 q^{11} - 6 q^{12} - 6 q^{14} - 16 q^{15} - 4 q^{16} - 28 q^{18} - 12 q^{19} + 2 q^{21} - 4 q^{22} - 6 q^{24} - 12 q^{29} + 22 q^{30} - 12 q^{33} + 12 q^{34} - 30 q^{35} + 20 q^{36} - 4 q^{37} - 6 q^{38} - 6 q^{40} - 42 q^{42} - 4 q^{43} - 66 q^{44} - 6 q^{45} - 12 q^{46} - 24 q^{47} - 4 q^{49} - 12 q^{50} - 10 q^{51} - 6 q^{52} - 90 q^{54} - 48 q^{56} + 2 q^{58} - 12 q^{59} + 66 q^{60} + 24 q^{62} + 48 q^{63} - 16 q^{64} + 54 q^{66} - 4 q^{67} - 6 q^{68} + 18 q^{69} + 26 q^{70} - 46 q^{72} + 78 q^{74} - 6 q^{75} - 6 q^{77} + 26 q^{78} - 8 q^{79} - 4 q^{81} - 24 q^{82} + 60 q^{83} + 18 q^{84} + 6 q^{85} - 66 q^{86} + 2 q^{88} - 108 q^{90} + 20 q^{91} - 12 q^{92} + 22 q^{93} - 6 q^{96} - 90 q^{98} - 26 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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