↑

Properties

Label 2736.2.ek
Level $2736$
Weight $2$
Character orbit 2736.ek
Rep. character $\chi_{2736}(221,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1904$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.ek (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 1936 1936 0
Cusp forms 1904 1904 0
Eisenstein series 32 32 0

Trace form

\( 1904 q - 6 q^{2} - 6 q^{3} + 2 q^{4} - 2 q^{6} + O(q^{10}) \) \( 1904 q - 6 q^{2} - 6 q^{3} + 2 q^{4} - 2 q^{6} - 12 q^{10} - 12 q^{11} - 6 q^{13} - 12 q^{14} - 12 q^{15} + 2 q^{16} - 12 q^{18} - 8 q^{19} - 54 q^{20} - 6 q^{21} + 14 q^{24} - 12 q^{28} - 12 q^{29} + 16 q^{30} - 6 q^{32} - 12 q^{33} - 30 q^{35} - 18 q^{36} - 6 q^{38} + 30 q^{42} + 2 q^{43} + 66 q^{44} - 18 q^{45} - 6 q^{48} + 896 q^{49} - 6 q^{51} - 6 q^{52} - 46 q^{54} - 4 q^{58} - 12 q^{59} - 6 q^{60} - 4 q^{61} + 12 q^{62} + 24 q^{63} - 16 q^{64} + 62 q^{66} - 6 q^{67} - 36 q^{68} + 18 q^{69} + 126 q^{72} - 90 q^{74} + 48 q^{75} - 26 q^{76} - 12 q^{77} - 6 q^{78} - 12 q^{79} - 48 q^{80} - 4 q^{81} + 4 q^{82} - 12 q^{83} + 22 q^{85} - 6 q^{86} + 102 q^{90} - 54 q^{91} - 6 q^{92} + 4 q^{93} + 24 q^{94} - 12 q^{95} - 132 q^{96} - 12 q^{97} + 54 q^{98} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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