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Properties

Label 2160.4.cq
Level $2160$
Weight $4$
Character orbit 2160.cq
Rep. character $\chi_{2160}(307,\cdot)$
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.cq (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

\( 1712 q + 2 q^{2} + 2 q^{5} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 1712 q + 2 q^{2} + 2 q^{5} - 4 q^{7} + 8 q^{8} + 24 q^{10} + 4 q^{11} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 2 q^{20} - 34 q^{22} + 4 q^{23} + 560 q^{26} - 264 q^{28} - 458 q^{32} - 396 q^{34} - 492 q^{35} - 16 q^{37} + 1222 q^{38} + 248 q^{40} - 4 q^{43} - 2368 q^{44} + 56 q^{46} + 2 q^{50} + 254 q^{52} - 16 q^{55} + 4 q^{56} - 34 q^{58} - 4 q^{61} - 3140 q^{62} - 1368 q^{64} + 4 q^{65} - 4 q^{67} + 550 q^{68} - 18 q^{70} + 32 q^{71} + 424 q^{74} - 1120 q^{76} - 5268 q^{80} - 40 q^{82} - 252 q^{85} + 4 q^{86} - 3114 q^{88} - 16 q^{91} + 3412 q^{92} - 4 q^{97} + 3996 q^{98} + O(q^{100}) \)

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

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