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Properties

Label 2160.2.ea
Level $2160$
Weight $2$
Character orbit 2160.ea
Rep. character $\chi_{2160}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $5136$
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.ea (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2160 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 5232 5232 0
Cusp forms 5136 5136 0
Eisenstein series 96 96 0

Trace form

\( 5136 q - 12 q^{2} - 12 q^{5} - 24 q^{6} - 24 q^{7} - 6 q^{8} + O(q^{10}) \) \( 5136 q - 12 q^{2} - 12 q^{5} - 24 q^{6} - 24 q^{7} - 6 q^{8} - 6 q^{10} - 24 q^{11} - 12 q^{12} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 54 q^{18} - 12 q^{20} - 24 q^{21} - 12 q^{22} - 24 q^{23} - 36 q^{24} - 48 q^{26} - 24 q^{28} - 30 q^{30} + 48 q^{32} - 24 q^{33} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 42 q^{40} - 72 q^{42} - 24 q^{43} + 48 q^{44} - 12 q^{45} - 12 q^{46} - 12 q^{48} - 12 q^{50} - 24 q^{51} - 12 q^{52} - 48 q^{55} - 24 q^{56} - 36 q^{57} - 12 q^{58} - 108 q^{60} - 24 q^{61} - 6 q^{62} - 24 q^{65} - 120 q^{66} - 24 q^{67} - 36 q^{68} - 24 q^{71} + 36 q^{72} + 24 q^{74} - 96 q^{75} - 24 q^{76} + 102 q^{78} + 156 q^{80} - 48 q^{81} - 24 q^{82} + 72 q^{84} + 18 q^{85} - 24 q^{86} - 24 q^{87} + 36 q^{88} - 42 q^{90} - 12 q^{91} - 126 q^{92} - 24 q^{93} + 84 q^{96} - 24 q^{97} + 108 q^{98} + O(q^{100}) \)

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.