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Properties

Label 1080.6.bs
Level $1080$
Weight $6$
Character orbit 1080.bs
Rep. character $\chi_{1080}(197,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1424$
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.bs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1296\)

Dimensions

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

Total New Old
Modular forms 4368 1456 2912
Cusp forms 4272 1424 2848
Eisenstein series 96 32 64

Trace form

\( 1424 q + 6 q^{2} - 4 q^{7} + O(q^{10}) \) \( 1424 q + 6 q^{2} - 4 q^{7} - 8 q^{10} - 4 q^{16} + 6 q^{20} + 126 q^{22} + 12 q^{23} - 4 q^{25} - 4104 q^{28} - 8 q^{31} + 14466 q^{32} + 198 q^{38} - 2 q^{40} + 24 q^{41} - 53896 q^{46} + 12 q^{47} + 6 q^{50} + 4094 q^{52} + 24984 q^{55} + 143232 q^{56} - 130 q^{58} + 12 q^{65} + 6150 q^{68} - 12502 q^{70} - 16 q^{73} - 54440 q^{76} - 136 q^{82} - 556728 q^{86} + 114006 q^{88} + 690960 q^{92} + 37512 q^{95} - 4 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)