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Properties

Label 2160.4.dc
Level $2160$
Weight $4$
Character orbit 2160.dc
Rep. character $\chi_{2160}(181,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.dc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 5232 1152 4080
Cusp forms 5136 1152 3984
Eisenstein series 96 0 96

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 544 q^{26} - 1960 q^{32} - 3080 q^{44} - 72 q^{46} + 3760 q^{47} + 28224 q^{49} + 2000 q^{56} - 1188 q^{58} + 2040 q^{59} + 7256 q^{62} - 1080 q^{64} - 3068 q^{68} - 3640 q^{74} - 1116 q^{76} + 4640 q^{80} + 2808 q^{82} - 2440 q^{83} - 520 q^{86} - 6080 q^{95} - 12104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{4}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)