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Properties

Label 1080.4.cc
Level $1080$
Weight $4$
Character orbit 1080.cc
Rep. character $\chi_{1080}(61,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2592$
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.cc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1080, [\chi])\).

Total New Old
Modular forms 3912 2592 1320
Cusp forms 3864 2592 1272
Eisenstein series 48 0 48

Trace form

\( 2592 q + O(q^{10}) \) \( 2592 q - 234 q^{12} - 150 q^{14} - 750 q^{24} + 1980 q^{26} - 120 q^{30} + 696 q^{33} - 2100 q^{36} - 1740 q^{38} - 120 q^{41} + 4740 q^{42} - 888 q^{44} + 5214 q^{48} - 2754 q^{52} - 4452 q^{54} + 3948 q^{56} + 1782 q^{58} + 1254 q^{62} + 120 q^{63} + 4944 q^{66} - 4818 q^{68} + 5964 q^{72} + 5460 q^{74} + 2262 q^{78} - 5610 q^{84} - 4158 q^{86} + 12168 q^{87} - 15960 q^{92} + 4050 q^{94} - 1362 q^{96} + O(q^{100}) \)

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

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