↑

Properties

Label 2169.2.db
Level $2169$
Weight $2$
Character orbit 2169.db
Rep. character $\chi_{2169}(232,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
Sturm bound $484$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.db (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2169 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 3904 3904 0
Cusp forms 3840 3840 0
Eisenstein series 64 64 0

Trace form

\( 3840 q - 24 q^{2} - 14 q^{3} + 1912 q^{4} - 10 q^{5} - 40 q^{6} - 6 q^{7} - 38 q^{9} + O(q^{10}) \) \( 3840 q - 24 q^{2} - 14 q^{3} + 1912 q^{4} - 10 q^{5} - 40 q^{6} - 6 q^{7} - 38 q^{9} - 12 q^{10} - 10 q^{11} - 4 q^{12} - 12 q^{13} - 26 q^{14} + 4 q^{15} - 1880 q^{16} - 32 q^{17} - 34 q^{18} - 6 q^{19} + 30 q^{20} - 62 q^{21} - 46 q^{22} - 2 q^{23} + 24 q^{24} - 470 q^{25} - 16 q^{26} - 38 q^{27} - 56 q^{28} - 22 q^{29} - 96 q^{30} - 16 q^{31} + 72 q^{32} - 18 q^{33} - 82 q^{34} + 84 q^{35} + 8 q^{36} - 36 q^{37} + 20 q^{38} - 4 q^{39} + 48 q^{40} - 10 q^{41} - 22 q^{42} - 28 q^{43} - 42 q^{44} + 16 q^{45} - 88 q^{46} - 10 q^{47} + 120 q^{48} - 70 q^{49} - 180 q^{50} + 22 q^{51} + 16 q^{52} - 28 q^{53} + 22 q^{54} - 24 q^{55} + 148 q^{56} - 76 q^{57} + 72 q^{58} - 10 q^{59} - 18 q^{60} - 46 q^{61} - 58 q^{62} + 116 q^{63} - 3664 q^{64} + 38 q^{65} + 22 q^{66} - 70 q^{67} + 46 q^{68} - 2 q^{69} - 48 q^{70} - 20 q^{71} - 172 q^{72} - 22 q^{73} - 40 q^{74} + 98 q^{75} + 208 q^{76} + 60 q^{77} + 154 q^{78} + 74 q^{79} + 144 q^{80} + 66 q^{81} - 18 q^{82} + 120 q^{83} + 74 q^{84} - 42 q^{85} + 6 q^{86} - 56 q^{87} + 52 q^{88} - 36 q^{89} - 150 q^{90} - 52 q^{91} + 16 q^{92} - 14 q^{93} - 30 q^{94} + 158 q^{95} + 16 q^{96} + 60 q^{98} + 54 q^{99} + O(q^{100}) \)

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.