Properties

Label 2160.2.cn
Level $2160$
Weight $2$
Character orbit 2160.cn
Rep. character $\chi_{2160}(557,\cdot)$
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.cn (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

\( 560 q + 6 q^{2} + 6 q^{5} + O(q^{10}) \) \( 560 q + 6 q^{2} + 6 q^{5} - 16 q^{10} + 12 q^{11} - 4 q^{13} - 4 q^{16} + 6 q^{20} - 10 q^{22} + 8 q^{28} - 8 q^{31} + 66 q^{32} + 12 q^{34} - 16 q^{37} - 6 q^{38} - 12 q^{40} - 40 q^{46} + 12 q^{47} + 6 q^{50} + 14 q^{52} + 12 q^{56} + 6 q^{58} - 4 q^{61} + 24 q^{64} + 12 q^{65} + 30 q^{68} - 6 q^{70} + 24 q^{74} + 8 q^{76} + 12 q^{83} + 8 q^{85} + 12 q^{86} - 42 q^{88} - 16 q^{91} + 120 q^{92} + 12 q^{95} - 4 q^{97} + O(q^{100}) \)

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

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