Properties

Label 1008.2.eo
Level 1008
Weight 2
Character orbit eo
Rep. character \(\chi_{1008}(85,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 576
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.eo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 144 \)
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 784 576 208
Cusp forms 752 576 176
Eisenstein series 32 0 32

Trace form

\( 576q + 12q^{6} + O(q^{10}) \) \( 576q + 12q^{6} - 24q^{12} - 28q^{20} + 32q^{24} + 64q^{26} - 24q^{27} + 8q^{30} - 32q^{36} - 56q^{38} - 48q^{46} - 52q^{48} + 288q^{49} + 52q^{50} + 36q^{58} - 24q^{59} - 68q^{60} - 24q^{62} + 72q^{64} - 56q^{66} - 52q^{68} - 116q^{72} - 28q^{74} - 112q^{75} - 24q^{76} - 116q^{78} - 304q^{80} + 72q^{82} - 124q^{86} + 48q^{88} - 8q^{90} + 76q^{92} + 48q^{93} - 128q^{95} - 32q^{96} - 64q^{99} + O(q^{100}) \)

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

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

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database