Properties

Label 1008.2.eh
Level 1008
Weight 2
Character orbit eh
Rep. character \(\chi_{1008}(11,\cdot)\)
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.eh (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

\( 752q - 2q^{3} - 4q^{4} - 6q^{5} - 8q^{6} - 4q^{7} + O(q^{10}) \) \( 752q - 2q^{3} - 4q^{4} - 6q^{5} - 8q^{6} - 4q^{7} - 4q^{10} - 6q^{11} - 2q^{12} - 4q^{13} - 6q^{14} - 4q^{16} - 8q^{18} - 4q^{19} - 12q^{20} + 2q^{21} - 4q^{22} - 12q^{23} - 22q^{24} - 8q^{27} - 16q^{28} - 12q^{29} - 26q^{30} - 4q^{33} - 8q^{34} - 30q^{35} - 20q^{36} - 4q^{37} - 6q^{38} - 4q^{39} + 2q^{40} - 42q^{42} - 4q^{43} + 66q^{44} + 18q^{45} + 4q^{46} + 32q^{48} - 4q^{49} - 12q^{50} + 6q^{51} + 2q^{52} + 14q^{54} - 32q^{55} + 36q^{56} + 2q^{58} + 42q^{60} - 4q^{61} - 16q^{64} - 6q^{66} - 4q^{67} - 54q^{68} - 2q^{69} + 26q^{70} - 46q^{72} - 90q^{74} + 6q^{75} - 4q^{76} - 6q^{77} + 34q^{78} - 4q^{81} - 72q^{83} - 82q^{84} - 14q^{85} - 66q^{86} - 4q^{87} + 2q^{88} - 80q^{90} + 20q^{91} - 12q^{92} + 22q^{93} - 36q^{94} + 138q^{96} - 8q^{97} + 114q^{98} - 26q^{99} + O(q^{100}) \)

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