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Properties

Label 1008.2.ea
Level $1008$
Weight $2$
Character orbit 1008.ea
Rep. character $\chi_{1008}(347,\cdot)$
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.ea (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

\( 752 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 752 q - 6 q^{2} - 2 q^{3} + 2 q^{4} - 8 q^{6} - 4 q^{7} - 4 q^{10} - 2 q^{12} - 4 q^{13} - 6 q^{14} + 2 q^{16} - 14 q^{18} - 4 q^{19} - 12 q^{20} - 16 q^{21} - 4 q^{22} - 22 q^{24} - 8 q^{27} - 16 q^{28} - 12 q^{29} + 46 q^{30} - 6 q^{32} - 4 q^{33} - 8 q^{34} + 30 q^{35} - 20 q^{36} - 4 q^{37} - 4 q^{39} - 4 q^{40} + 18 q^{42} - 4 q^{43} - 66 q^{44} - 42 q^{45} + 4 q^{46} + 32 q^{48} - 4 q^{49} - 12 q^{50} - 54 q^{51} - 4 q^{52} - 118 q^{54} - 32 q^{55} + 36 q^{56} - 4 q^{58} - 6 q^{59} - 66 q^{60} + 2 q^{61} - 16 q^{64} - 12 q^{65} + 30 q^{66} + 2 q^{67} - 2 q^{69} - 16 q^{70} - 46 q^{72} + 12 q^{75} - 4 q^{76} - 6 q^{77} + 34 q^{78} - 4 q^{81} - 72 q^{83} + 44 q^{84} - 14 q^{85} - 4 q^{87} - 4 q^{88} - 80 q^{90} + 20 q^{91} - 12 q^{92} - 14 q^{93} + 18 q^{94} + 36 q^{96} - 8 q^{97} - 114 q^{98} - 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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