Properties

Label 1008.2.ef
Level 1008
Weight 2
Character orbit ef
Rep. character \(\chi_{1008}(115,\cdot)\)
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.ef (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

\( 752q - 4q^{2} - 6q^{3} - 4q^{4} - 6q^{5} - 4q^{7} - 16q^{8} + O(q^{10}) \) \( 752q - 4q^{2} - 6q^{3} - 4q^{4} - 6q^{5} - 4q^{7} - 16q^{8} - 12q^{10} + 2q^{11} - 6q^{12} - 18q^{14} - 4q^{16} - 24q^{17} + 4q^{18} - 12q^{19} - 10q^{21} - 4q^{22} + 4q^{23} - 6q^{24} - 12q^{26} - 16q^{28} - 4q^{29} - 18q^{30} + 36q^{32} - 12q^{33} - 12q^{34} + 2q^{35} - 20q^{36} - 4q^{37} - 6q^{38} - 4q^{39} - 6q^{40} - 46q^{42} - 4q^{43} - 26q^{44} - 6q^{45} - 12q^{46} - 4q^{49} + 4q^{50} - 34q^{51} - 6q^{52} - 4q^{53} + 78q^{54} + 24q^{56} + 2q^{58} - 30q^{60} - 16q^{64} - 8q^{65} - 66q^{66} - 4q^{67} - 6q^{68} + 18q^{69} - 30q^{70} - 32q^{71} - 14q^{72} - 26q^{74} - 6q^{75} + 26q^{77} - 50q^{78} - 12q^{80} - 4q^{81} + 60q^{83} - 2q^{84} - 14q^{85} + 22q^{86} - 12q^{87} + 2q^{88} - 108q^{90} - 36q^{91} - 20q^{92} - 26q^{93} - 6q^{96} + 22q^{98} + 10q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database