Properties

Label 16.12.b
Level 16
Weight 12
Character orbit b
Rep. character \(\chi_{16}(9,\cdot)\)
Character field \(\Q\)
Dimension 0
Newforms 0
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 0 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(16, [\chi])\).

Total New Old
Modular forms 24 0 24
Cusp forms 20 0 20
Eisenstein series 4 0 4

Decomposition of \(S_{12}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)