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Properties

Label 1080.6.ct
Level $1080$
Weight $6$
Character orbit 1080.ct
Rep. character $\chi_{1080}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $12912$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1080.ct (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1080 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1080, [\chi])\).

Total New Old
Modular forms 13008 13008 0
Cusp forms 12912 12912 0
Eisenstein series 96 96 0

Trace form

\( 12912 q - 12 q^{2} - 24 q^{3} - 24 q^{6} - 6 q^{8} + O(q^{10}) \) \( 12912 q - 12 q^{2} - 24 q^{3} - 24 q^{6} - 6 q^{8} - 6 q^{10} - 48 q^{11} - 12 q^{12} - 24 q^{16} - 12 q^{17} - 11394 q^{18} - 12 q^{20} - 12 q^{22} - 24 q^{25} - 48 q^{26} - 24 q^{27} - 24 q^{28} - 12 q^{30} + 14448 q^{32} - 24 q^{33} - 12 q^{35} - 24 q^{36} - 204 q^{38} - 12 q^{40} - 48 q^{41} - 120552 q^{42} - 24 q^{43} - 12 q^{46} - 12 q^{48} - 12 q^{50} - 48 q^{51} - 12 q^{52} + 286416 q^{56} - 2940 q^{57} - 12 q^{58} + 212328 q^{60} - 6 q^{62} - 24 q^{65} + 52296 q^{66} - 24 q^{67} - 6156 q^{68} - 12 q^{70} - 196620 q^{72} - 12 q^{73} + 383184 q^{75} - 12312 q^{76} - 594870 q^{78} + 1166196 q^{80} - 48 q^{81} - 24 q^{82} - 24 q^{83} + 556716 q^{86} + 196596 q^{88} + 538428 q^{90} - 24 q^{91} - 690966 q^{92} + 269436 q^{96} - 24 q^{97} + 871980 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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