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Properties

Label 1080.2.bd
Level $1080$
Weight $2$
Character orbit 1080.bd
Rep. character $\chi_{1080}(179,\cdot)$
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.bd (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

\( 136 q - 2 q^{4} + O(q^{10}) \) \( 136 q - 2 q^{4} - 8 q^{10} + 12 q^{11} + 6 q^{14} - 2 q^{16} - 16 q^{19} + 24 q^{20} - 2 q^{25} + 4 q^{40} + 12 q^{41} - 4 q^{46} - 48 q^{49} + 42 q^{50} + 6 q^{56} + 12 q^{59} + 4 q^{64} + 6 q^{65} + 60 q^{74} - 16 q^{76} + 40 q^{91} + 14 q^{94} + O(q^{100}) \)

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

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