Properties

Label 1008.2.du
Level 1008
Weight 2
Character orbit du
Rep. character \(\chi_{1008}(37,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 312
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.du (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 112 \)
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 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312q + 2q^{2} - 4q^{4} + 2q^{5} - 4q^{8} + O(q^{10}) \) \( 312q + 2q^{2} - 4q^{4} + 2q^{5} - 4q^{8} + 4q^{10} - 2q^{11} - 8q^{13} - 8q^{14} + 4q^{17} - 2q^{19} + 24q^{20} + 12q^{22} + 2q^{26} + 10q^{28} + 24q^{29} + 20q^{31} - 8q^{32} + 32q^{34} + 26q^{35} - 10q^{37} + 22q^{38} - 54q^{40} - 16q^{43} + 34q^{44} + 44q^{47} - 8q^{49} + 56q^{50} + 28q^{52} + 10q^{53} - 16q^{56} + 26q^{58} - 14q^{59} - 2q^{61} + 116q^{62} - 16q^{64} + 4q^{65} + 14q^{67} - 4q^{68} + 28q^{70} + 22q^{74} - 20q^{76} + 18q^{77} - 4q^{79} - 48q^{80} + 22q^{82} - 32q^{83} + 12q^{85} - 26q^{88} - 16q^{91} + 116q^{92} + 66q^{94} + 28q^{95} - 16q^{97} - 96q^{98} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database