Properties

Label 8.9.c
Level $8$
Weight $9$
Character orbit 8.c
Rep. character $\chi_{8}(7,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 8.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(8, [\chi])\).

Total New Old
Modular forms 10 0 10
Cusp forms 6 0 6
Eisenstein series 4 0 4

Decomposition of \(S_{9}^{\mathrm{old}}(8, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(8, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)