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Properties

Label 1080.2.bk
Level $1080$
Weight $2$
Character orbit 1080.bk
Rep. character $\chi_{1080}(469,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

Total New Old
Modular forms 456 152 304
Cusp forms 408 136 272
Eisenstein series 48 16 32

Trace form

\( 136 q - 2 q^{4} + O(q^{10}) \) \( 136 q - 2 q^{4} + 10 q^{14} - 2 q^{16} + 2 q^{20} - 2 q^{25} - 16 q^{26} - 4 q^{31} + 8 q^{34} - 6 q^{40} + 4 q^{41} + 56 q^{44} - 28 q^{46} + 40 q^{49} + 12 q^{50} - 28 q^{55} - 26 q^{56} - 20 q^{64} - 18 q^{65} - 6 q^{70} + 128 q^{71} - 36 q^{74} + 12 q^{76} - 4 q^{79} + 36 q^{80} - 44 q^{86} + 32 q^{89} - 34 q^{94} - 8 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

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