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Properties

Label 1080.4.bm
Level $1080$
Weight $4$
Character orbit 1080.bm
Rep. character $\chi_{1080}(251,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
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 288 1032
Cusp forms 1272 288 984
Eisenstein series 48 0 48

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 150 q^{14} - 3600 q^{25} - 198 q^{34} - 1740 q^{38} - 90 q^{40} + 120 q^{41} - 36 q^{46} + 7056 q^{49} - 918 q^{52} + 1974 q^{56} + 594 q^{58} + 6120 q^{59} + 1224 q^{64} - 108 q^{68} + 5460 q^{74} + 558 q^{76} - 1404 q^{82} + 7320 q^{83} + 4158 q^{86} + 7980 q^{92} - 1350 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)