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Properties

Label 1080.4.bs
Level $1080$
Weight $4$
Character orbit 1080.bs
Rep. character $\chi_{1080}(197,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.bs (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1080, [\chi])\).

Total New Old
Modular forms 2640 880 1760
Cusp forms 2544 848 1696
Eisenstein series 96 32 64

Trace form

\( 848 q + 6 q^{2} - 4 q^{7} + O(q^{10}) \) \( 848 q + 6 q^{2} - 4 q^{7} - 8 q^{10} - 4 q^{16} + 6 q^{20} + 30 q^{22} + 12 q^{23} - 4 q^{25} - 264 q^{28} - 8 q^{31} - 1374 q^{32} + 54 q^{38} - 2 q^{40} + 24 q^{41} + 56 q^{46} + 12 q^{47} + 6 q^{50} + 254 q^{52} + 984 q^{55} - 3936 q^{56} - 34 q^{58} + 12 q^{65} + 390 q^{68} - 502 q^{70} - 16 q^{73} + 856 q^{76} - 40 q^{82} + 8328 q^{86} - 3114 q^{88} - 9456 q^{92} + 1512 q^{95} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)