Properties

Label 8008.2.mp
Level $8008$
Weight $2$
Character orbit 8008.mp
Rep. character $\chi_{8008}(95,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $0$
Newform subspaces $0$
Sturm bound $2688$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8008.mp (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4004 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 0 \)
Sturm bound: \(2688\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8008, [\chi])\).

Total New Old
Modular forms 10880 0 10880
Cusp forms 10624 0 10624
Eisenstein series 256 0 256

Decomposition of \(S_{2}^{\mathrm{old}}(8008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4004, [\chi])\)\(^{\oplus 2}\)