Properties

Label 16.9.d
Level $16$
Weight $9$
Character orbit 16.d
Rep. character $\chi_{16}(7,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 16.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(16, [\chi])\).

Total New Old
Modular forms 18 0 18
Cusp forms 14 0 14
Eisenstein series 4 0 4

Decomposition of \(S_{9}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)