Properties

Label 4008.2.bf
Level $4008$
Weight $2$
Character orbit 4008.bf
Rep. character $\chi_{4008}(55,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $0$
Newform subspaces $0$
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.bf (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 668 \)
Character field: \(\Q(\zeta_{166})\)
Newform subspaces: \( 0 \)
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

\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2004, [\chi])\)\(^{\oplus 2}\)