Properties

Label 8008.2.bn
Level $8008$
Weight $2$
Character orbit 8008.bn
Rep. character $\chi_{8008}(463,\cdot)$
Character field $\Q(\zeta_{4})$
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.bn (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(i)\)
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 2720 0 2720
Cusp forms 2656 0 2656
Eisenstein series 64 0 64

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

\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4004, [\chi])\)\(^{\oplus 2}\)