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Properties

Label 2160.2.cf
Level $2160$
Weight $2$
Character orbit 2160.cf
Rep. character $\chi_{2160}(469,\cdot)$
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.cf (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

\( 560 q - 4 q^{4} + 2 q^{5} + O(q^{10}) \) \( 560 q - 4 q^{4} + 2 q^{5} - 8 q^{10} + 4 q^{11} - 12 q^{14} - 4 q^{16} - 16 q^{19} + 16 q^{20} + 48 q^{26} + 4 q^{29} - 8 q^{31} + 4 q^{34} - 12 q^{35} - 2 q^{40} + 16 q^{44} + 24 q^{46} - 240 q^{49} - 32 q^{50} + 32 q^{56} + 4 q^{59} - 4 q^{61} - 16 q^{64} + 4 q^{65} - 16 q^{70} + 4 q^{74} + 8 q^{76} - 8 q^{79} - 112 q^{80} + 8 q^{85} + 44 q^{86} + 40 q^{91} - 20 q^{94} + 4 q^{95} + O(q^{100}) \)

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

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