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Properties

Label 1080.2.bp
Level $1080$
Weight $2$
Character orbit 1080.bp
Rep. character $\chi_{1080}(307,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $272$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 912 304 608
Cusp forms 816 272 544
Eisenstein series 96 32 64

Trace form

\( 272 q + 2 q^{2} + 8 q^{8} + O(q^{10}) \) \( 272 q + 2 q^{2} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 4 q^{16} + 16 q^{17} - 14 q^{20} + 6 q^{22} - 4 q^{25} + 48 q^{26} + 8 q^{28} + 22 q^{32} + 16 q^{35} + 26 q^{38} - 2 q^{40} + 8 q^{41} - 4 q^{43} - 40 q^{46} + 42 q^{50} + 14 q^{52} - 24 q^{56} + 6 q^{58} + 76 q^{62} + 4 q^{65} - 4 q^{67} + 46 q^{68} + 18 q^{70} - 16 q^{73} - 92 q^{80} + 4 q^{83} + 40 q^{86} - 42 q^{88} - 32 q^{91} - 52 q^{92} - 4 q^{97} + 140 q^{98} + O(q^{100}) \)

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

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