Properties

Label 384.1.b
Level $384$
Weight $1$
Character orbit 384.b
Rep. character $\chi_{384}(319,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 384.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(384, [\chi])\).

Total New Old
Modular forms 18 0 18
Cusp forms 2 0 2
Eisenstein series 16 0 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 0

Decomposition of \(S_{1}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)