Properties

Label 64.8.g
Level $64$
Weight $8$
Character orbit 64.g
Rep. character $\chi_{64}(9,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $0$
Newform subspaces $0$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 64.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 0 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(64, [\chi])\).

Total New Old
Modular forms 232 0 232
Cusp forms 216 0 216
Eisenstein series 16 0 16

Decomposition of \(S_{8}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)