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Properties

Label 2160.4.du
Level $2160$
Weight $4$
Character orbit 2160.du
Rep. character $\chi_{2160}(59,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $15504$
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.du (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2160 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2160, [\chi])\).

Total New Old
Modular forms 15600 15600 0
Cusp forms 15504 15504 0
Eisenstein series 96 96 0

Trace form

\( 15504 q - 24 q^{4} - 12 q^{5} - 24 q^{6} + O(q^{10}) \) \( 15504 q - 24 q^{4} - 12 q^{5} - 24 q^{6} - 6 q^{10} - 24 q^{11} - 24 q^{14} - 24 q^{16} - 12 q^{19} + 450 q^{20} - 24 q^{21} - 24 q^{24} - 24 q^{29} - 12 q^{30} + 72 q^{34} - 18 q^{35} - 24 q^{36} - 48 q^{39} - 12 q^{40} - 36 q^{44} - 12 q^{45} - 12 q^{46} - 48 q^{49} + 6384 q^{50} + 300 q^{51} - 8928 q^{54} - 48 q^{55} + 4092 q^{56} - 24 q^{59} - 3672 q^{60} - 24 q^{61} - 12 q^{64} - 24 q^{65} + 2484 q^{66} - 24 q^{69} - 2070 q^{70} - 72 q^{71} - 24 q^{74} - 4968 q^{75} - 24 q^{76} - 48 q^{81} + 13428 q^{84} + 738 q^{85} + 16656 q^{86} - 4386 q^{90} - 12 q^{91} - 24 q^{94} - 5100 q^{96} - 24 q^{99} + O(q^{100}) \)

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.