↑

Properties

Label 1080.4.cj
Level $1080$
Weight $4$
Character orbit 1080.cj
Rep. character $\chi_{1080}(229,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $3864$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.cj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1080 \)
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 3912 0
Cusp forms 3864 3864 0
Eisenstein series 48 48 0

Trace form

\( 3864 q - 12 q^{4} - 12 q^{6} - 24 q^{9} + O(q^{10}) \) \( 3864 q - 12 q^{4} - 12 q^{6} - 24 q^{9} - 3 q^{10} - 12 q^{14} - 12 q^{15} - 12 q^{16} + 225 q^{20} + 150 q^{24} - 12 q^{25} - 24 q^{26} + 75 q^{30} - 24 q^{31} - 60 q^{34} - 12 q^{36} - 24 q^{39} + 369 q^{40} - 24 q^{41} - 894 q^{44} - 6 q^{46} - 24 q^{49} - 3204 q^{50} - 4464 q^{54} - 24 q^{55} - 6018 q^{56} + 2682 q^{60} - 6 q^{64} - 12 q^{65} - 1266 q^{66} - 1011 q^{70} - 11940 q^{71} - 6306 q^{74} - 396 q^{76} - 24 q^{79} + 78 q^{80} - 24 q^{81} - 7062 q^{84} - 4194 q^{86} - 12 q^{89} - 1104 q^{90} - 12 q^{94} - 762 q^{95} - 2550 q^{96} + O(q^{100}) \)

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.