Properties

Label 2160.4.dp
Level $2160$
Weight $4$
Character orbit 2160.dp
Rep. character $\chi_{2160}(169,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $0$
Newform subspaces $0$
Sturm bound $1728$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.dp (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1080 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 0 \)
Sturm bound: \(1728\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).

Total New Old
Modular forms 7824 0 7824
Cusp forms 7728 0 7728
Eisenstein series 96 0 96

Decomposition of \(S_{4}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)