Properties

Label 1008.2.ei
Level 1008
Weight 2
Character orbit ei
Rep. character \(\chi_{1008}(107,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 256
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.ei (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
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 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

Trace form

\( 256q + O(q^{10}) \) \( 256q + 8q^{16} + 48q^{22} + 24q^{28} - 64q^{34} - 24q^{40} - 24q^{52} + 40q^{58} + 96q^{64} + 16q^{67} - 48q^{70} + 48q^{76} + 40q^{82} + 8q^{88} - 48q^{91} - 120q^{94} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database