↑

Properties

Label 2169.2.cl
Level $2169$
Weight $2$
Character orbit 2169.cl
Rep. character $\chi_{2169}(322,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $484$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.cl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2169 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(484\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2169, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1920 1920 0
Eisenstein series 32 32 0

Trace form

\( 1920 q + 8 q^{2} - 7 q^{3} + 1896 q^{4} + q^{5} - 22 q^{6} - 5 q^{7} - 19 q^{9} + O(q^{10}) \) \( 1920 q + 8 q^{2} - 7 q^{3} + 1896 q^{4} + q^{5} - 22 q^{6} - 5 q^{7} - 19 q^{9} - 30 q^{10} - 49 q^{12} - 10 q^{13} - 65 q^{14} + 5 q^{15} + 1848 q^{16} - 20 q^{17} - 24 q^{18} - 63 q^{19} - 72 q^{20} - 8 q^{21} - 5 q^{23} - 33 q^{24} + 229 q^{25} - 30 q^{26} - 31 q^{27} - 50 q^{28} + 3 q^{29} - 16 q^{30} - 14 q^{31} + 68 q^{32} - 36 q^{33} + 15 q^{34} - 71 q^{35} - 36 q^{36} - 11 q^{37} - 18 q^{38} - 7 q^{39} - 66 q^{40} - 12 q^{41} - 129 q^{42} - 4 q^{43} + 2 q^{45} - 30 q^{46} - q^{47} - 227 q^{48} + 487 q^{49} - 135 q^{50} - 10 q^{51} - 115 q^{52} - 6 q^{53} + 99 q^{54} - 22 q^{55} - 190 q^{56} + 65 q^{57} - 9 q^{58} + 11 q^{59} - 86 q^{60} + 5 q^{61} - 111 q^{62} - 102 q^{63} + 1752 q^{64} - 45 q^{65} + 79 q^{66} - q^{67} - 40 q^{68} + 96 q^{69} - 12 q^{70} - 23 q^{71} - 232 q^{72} - 20 q^{73} - 12 q^{74} - 193 q^{75} - 234 q^{76} + 23 q^{77} - 53 q^{78} + 42 q^{79} - 218 q^{80} - 7 q^{81} - 45 q^{82} + 98 q^{83} - 112 q^{84} + 31 q^{85} - 5 q^{86} - 64 q^{87} - 33 q^{89} - 150 q^{90} - 56 q^{91} - 38 q^{92} + 5 q^{93} - 36 q^{94} + 55 q^{95} - 54 q^{96} - 46 q^{97} + 4 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2169, [\chi])\) into newform subspaces

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