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Properties

Label 2160.2.cq
Level $2160$
Weight $2$
Character orbit 2160.cq
Rep. character $\chi_{2160}(307,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.cq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

Total New Old
Modular forms 1776 592 1184
Cusp forms 1680 560 1120
Eisenstein series 96 32 64

Trace form

\( 560 q + 2 q^{2} + 2 q^{5} - 4 q^{7} + 8 q^{8} + O(q^{10}) \) \( 560 q + 2 q^{2} + 2 q^{5} - 4 q^{7} + 8 q^{8} + 4 q^{11} - 4 q^{13} - 4 q^{16} + 16 q^{17} + 2 q^{20} - 10 q^{22} + 4 q^{23} - 16 q^{26} - 24 q^{28} + 22 q^{32} + 12 q^{34} - 12 q^{35} - 16 q^{37} + 34 q^{38} + 8 q^{40} - 4 q^{43} - 64 q^{44} + 8 q^{46} + 2 q^{50} + 14 q^{52} - 16 q^{55} + 4 q^{56} - 10 q^{58} - 4 q^{61} + 76 q^{62} - 24 q^{64} + 4 q^{65} - 4 q^{67} + 46 q^{68} - 6 q^{70} + 32 q^{71} + 64 q^{74} - 16 q^{76} + 204 q^{80} - 16 q^{82} - 12 q^{85} + 4 q^{86} + 6 q^{88} - 16 q^{91} - 20 q^{92} - 4 q^{97} - 108 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

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