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Properties

Label 2160.4.cr
Level $2160$
Weight $4$
Character orbit 2160.cr
Rep. character $\chi_{2160}(197,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.cr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
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 1744 3488
Cusp forms 5136 1712 3424
Eisenstein series 96 32 64

Trace form

\( 1712 q + 6 q^{2} + 6 q^{5} + O(q^{10}) \) \( 1712 q + 6 q^{2} + 6 q^{5} + 24 q^{10} + 12 q^{11} - 4 q^{16} + 6 q^{20} + 30 q^{22} + 248 q^{28} - 8 q^{31} + 1386 q^{32} + 396 q^{34} + 54 q^{38} + 248 q^{40} - 4 q^{43} - 88 q^{46} + 12 q^{47} + 6 q^{50} - 258 q^{52} + 12 q^{56} - 34 q^{58} - 4 q^{61} - 1368 q^{64} + 12 q^{65} - 4 q^{67} + 390 q^{68} + 14 q^{70} - 96 q^{74} + 1112 q^{76} + 12 q^{77} + 24 q^{82} - 252 q^{85} + 12 q^{86} + 3110 q^{88} - 16 q^{91} - 9456 q^{92} + 12 q^{95} - 4 q^{97} + O(q^{100}) \)

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

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