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Properties

Label 1080.6.co
Level $1080$
Weight $6$
Character orbit 1080.co
Rep. character $\chi_{1080}(77,\cdot)$
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.co (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

\( 12912 q - 12 q^{2} - 24 q^{6} - 24 q^{7} - 18 q^{8} + O(q^{10}) \) \( 12912 q - 12 q^{2} - 24 q^{6} - 24 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{12} - 24 q^{15} - 24 q^{16} - 36 q^{17} + 11370 q^{18} - 12 q^{20} - 12 q^{22} - 24 q^{23} - 24 q^{25} - 24 q^{28} - 12 q^{30} - 48 q^{31} + 14448 q^{32} - 24 q^{33} - 24 q^{36} + 180 q^{38} - 12 q^{40} - 48 q^{41} - 120552 q^{42} - 12 q^{46} - 24 q^{47} - 12 q^{48} - 12 q^{50} - 12 q^{52} - 48 q^{55} - 286464 q^{56} + 2892 q^{57} - 12 q^{58} + 212328 q^{60} - 18 q^{62} - 24 q^{63} - 24 q^{65} - 52344 q^{66} + 6132 q^{68} - 12 q^{70} - 72 q^{71} + 196596 q^{72} - 12 q^{73} + 12264 q^{76} + 589014 q^{78} - 48 q^{81} - 24 q^{82} - 556764 q^{86} - 24 q^{87} + 196596 q^{88} - 1247040 q^{90} + 690942 q^{92} + 37476 q^{95} - 269484 q^{96} - 24 q^{97} + 2615940 q^{98} + O(q^{100}) \)

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.