Properties

Label 1008.2.ek
Level 1008
Weight 2
Character orbit ek
Rep. character \(\chi_{1008}(187,\cdot)\)
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.ek (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

\( 752q + 2q^{2} - 6q^{3} + 2q^{4} - 4q^{7} - 16q^{8} + O(q^{10}) \) \( 752q + 2q^{2} - 6q^{3} + 2q^{4} - 4q^{7} - 16q^{8} - 12q^{10} - 4q^{11} - 6q^{12} + 6q^{14} + 2q^{16} - 24q^{17} + 10q^{18} - 12q^{19} + 8q^{21} - 4q^{22} - 8q^{23} - 6q^{24} - 12q^{26} - 16q^{28} - 4q^{29} + 30q^{30} - 18q^{32} - 12q^{33} + 12q^{34} + 2q^{35} - 20q^{36} - 4q^{37} - 4q^{39} + 14q^{42} - 4q^{43} - 26q^{44} - 6q^{45} - 12q^{46} - 4q^{49} + 4q^{50} + 26q^{51} - 4q^{53} + 78q^{54} - 96q^{56} - 4q^{58} - 6q^{59} + 30q^{60} - 6q^{61} - 16q^{64} + 4q^{65} - 6q^{66} + 2q^{67} - 18q^{69} + 12q^{70} - 32q^{71} - 14q^{72} + 52q^{74} - 36q^{75} - 58q^{77} - 50q^{78} - 12q^{80} - 4q^{81} - 60q^{83} - 128q^{84} - 14q^{85} - 44q^{86} - 12q^{87} - 4q^{88} + 108q^{90} - 36q^{91} - 20q^{92} + 10q^{93} - 6q^{94} - 108q^{96} + 22q^{98} + 10q^{99} + O(q^{100}) \)

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