Properties

Label 1008.2.bb
Level 1008
Weight 2
Character orbit bb
Rep. character \(\chi_{1008}(125,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 128
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.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 400 128 272
Cusp forms 368 128 240
Eisenstein series 32 0 32

Trace form

\( 128q + O(q^{10}) \) \( 128q - 8q^{16} - 48q^{22} + 24q^{28} - 72q^{58} + 96q^{64} - 16q^{67} + 24q^{70} + 8q^{88} - 48q^{91} + O(q^{100}) \)

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