Properties

Label 1008.2.dx
Level 1008
Weight 2
Character orbit dx
Rep. character \(\chi_{1008}(277,\cdot)\)
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.dx (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

\( 752q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 8q^{6} - 16q^{8} + O(q^{10}) \) \( 752q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 8q^{6} - 16q^{8} - 4q^{10} + 2q^{11} - 2q^{12} - 4q^{13} + 14q^{14} - 16q^{15} - 4q^{16} - 8q^{17} + 24q^{18} - 4q^{19} - 4q^{20} - 10q^{21} - 4q^{22} + 18q^{24} - 4q^{26} - 8q^{27} - 4q^{29} + 14q^{30} - 8q^{31} - 44q^{32} - 4q^{33} + 2q^{35} + 20q^{36} - 4q^{37} + 2q^{38} + 2q^{40} - 46q^{42} - 4q^{43} + 18q^{44} - 22q^{45} + 4q^{46} + 152q^{47} - 48q^{48} - 4q^{49} + 4q^{50} + 30q^{51} + 2q^{52} - 4q^{53} + 70q^{54} + 52q^{56} + 2q^{58} - 4q^{59} - 86q^{60} - 4q^{61} - 112q^{62} + 48q^{63} - 16q^{64} - 8q^{65} + 2q^{66} - 4q^{67} - 14q^{68} - 2q^{69} - 30q^{70} - 14q^{72} + 30q^{74} + 6q^{75} - 4q^{76} - 30q^{77} - 42q^{78} - 8q^{79} - 4q^{80} - 4q^{81} - 8q^{82} + 16q^{83} + 50q^{84} + 6q^{85} + 22q^{86} + 2q^{88} - 80q^{90} - 36q^{91} + 12q^{92} - 26q^{93} - 36q^{94} - 8q^{95} - 6q^{96} - 8q^{97} - 46q^{98} + 10q^{99} + O(q^{100}) \)

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