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Properties

Label 1080.2.cc
Level $1080$
Weight $2$
Character orbit 1080.cc
Rep. character $\chi_{1080}(61,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $864$
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.cc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 1320 864 456
Cusp forms 1272 864 408
Eisenstein series 48 0 48

Trace form

\( 864 q + O(q^{10}) \) \( 864 q - 18 q^{12} + 30 q^{14} - 30 q^{24} + 36 q^{26} + 24 q^{30} - 24 q^{33} + 60 q^{36} + 60 q^{38} + 24 q^{41} + 60 q^{42} - 24 q^{44} - 114 q^{48} + 54 q^{52} + 84 q^{54} - 84 q^{56} - 54 q^{58} + 66 q^{62} + 120 q^{63} + 48 q^{66} - 138 q^{68} - 84 q^{72} - 84 q^{74} - 78 q^{78} - 66 q^{84} + 54 q^{86} + 72 q^{87} - 120 q^{92} + 54 q^{94} - 210 q^{96} + O(q^{100}) \)

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

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