Properties

Label 4008.2.bc
Level 4008
Weight 2
Character orbit bc
Rep. character \(\chi_{4008}(47,\cdot)\)
Character field \(\Q(\zeta_{166})\)
Dimension 0
Newforms 0
Sturm bound 1344
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.bc (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2004 \)
Character field: \(\Q(\zeta_{166})\)
Newforms: \( 0 \)
Sturm bound: \(1344\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4008, [\chi])\).

Total New Old
Modular forms 55760 0 55760
Cusp forms 54448 0 54448
Eisenstein series 1312 0 1312

Decomposition of \(S_{2}^{\mathrm{old}}(4008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2004, [\chi])\)\(^{\oplus 2}\)