Properties

Label 1368.2.et
Level $1368$
Weight $2$
Character orbit 1368.et
Rep. character $\chi_{1368}(173,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1416$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.et (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 1464 1464 0
Cusp forms 1416 1416 0
Eisenstein series 48 48 0

Trace form

\( 1416 q - 9 q^{2} - 3 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} + O(q^{10}) \) \( 1416 q - 9 q^{2} - 3 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} - 12 q^{10} - 9 q^{12} - 9 q^{14} - 12 q^{15} - 3 q^{16} - 18 q^{20} + 9 q^{22} - 18 q^{23} - 57 q^{24} - 6 q^{25} + 72 q^{26} - 24 q^{28} - 6 q^{30} - 18 q^{31} - 9 q^{32} + 6 q^{33} + 15 q^{34} - 66 q^{36} - 9 q^{38} - 24 q^{39} + 12 q^{40} + 18 q^{41} - 6 q^{42} + 135 q^{44} - 18 q^{46} - 18 q^{47} + 48 q^{48} + 1260 q^{49} - 9 q^{50} - 3 q^{52} + 54 q^{54} - 54 q^{55} - 63 q^{56} - 12 q^{57} - 6 q^{58} + 9 q^{60} - 18 q^{62} - 96 q^{63} - 24 q^{64} - 18 q^{65} - 18 q^{66} - 24 q^{70} + 60 q^{72} - 24 q^{73} - 90 q^{74} - 3 q^{76} + 27 q^{78} - 6 q^{79} - 12 q^{82} - 9 q^{84} - 9 q^{86} - 6 q^{87} - 141 q^{90} - 9 q^{92} - 18 q^{95} + 63 q^{96} - 6 q^{97} - 81 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.