Properties

Label 1008.2.dm
Level 1008
Weight 2
Character orbit dm
Rep. character \(\chi_{1008}(155,\cdot)\)
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.dm (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

\( 576q - 12q^{6} + O(q^{10}) \) \( 576q - 12q^{6} + 24q^{12} + 84q^{20} + 32q^{24} + 24q^{27} + 48q^{30} + 8q^{36} + 48q^{39} + 48q^{46} - 52q^{48} - 288q^{49} - 156q^{50} - 36q^{58} + 72q^{59} - 68q^{60} + 72q^{64} - 184q^{66} - 156q^{68} + 4q^{72} - 84q^{74} + 112q^{75} + 24q^{76} - 116q^{78} + 72q^{82} - 60q^{86} - 112q^{87} - 48q^{88} + 8q^{90} - 228q^{92} + 48q^{93} + 32q^{96} - 64q^{99} + O(q^{100}) \)

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