Properties

Label 384.4.s
Level $384$
Weight $4$
Character orbit 384.s
Rep. character $\chi_{384}(23,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $0$
Newform subspaces $0$
Sturm bound $256$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 384.s (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 0 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(384, [\chi])\).

Total New Old
Modular forms 1568 0 1568
Cusp forms 1504 0 1504
Eisenstein series 64 0 64

Decomposition of \(S_{4}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)