Properties

Label 384.5.q
Level $384$
Weight $5$
Character orbit 384.q
Rep. character $\chi_{384}(41,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $0$
Newform subspaces $0$
Sturm bound $320$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 384.q (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 0 \)
Sturm bound: \(320\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(384, [\chi])\).

Total New Old
Modular forms 2080 0 2080
Cusp forms 2016 0 2016
Eisenstein series 64 0 64

Decomposition of \(S_{5}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)