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Properties

Label 1080.4.bk
Level $1080$
Weight $4$
Character orbit 1080.bk
Rep. character $\chi_{1080}(469,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $424$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1320 440 880
Cusp forms 1272 424 848
Eisenstein series 48 16 32

Trace form

\( 424 q - 2 q^{4} + O(q^{10}) \) \( 424 q - 2 q^{4} + 12 q^{10} + 34 q^{14} - 2 q^{16} + 206 q^{20} - 2 q^{25} + 248 q^{26} - 4 q^{31} - 184 q^{34} - 126 q^{40} + 4 q^{41} + 1448 q^{44} - 76 q^{46} + 9208 q^{49} + 1170 q^{50} - 508 q^{55} - 26 q^{56} - 692 q^{64} - 498 q^{65} + 84 q^{70} - 7936 q^{71} - 2292 q^{74} + 684 q^{76} - 4 q^{79} + 3012 q^{80} - 1424 q^{86} - 832 q^{89} + 1622 q^{94} - 248 q^{95} + O(q^{100}) \)

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

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