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Properties

Label 2169.2.da
Level $2169$
Weight $2$
Character orbit 2169.da
Rep. character $\chi_{2169}(25,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.da (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

\( 3840 q - 20 q^{3} + 1888 q^{4} - 10 q^{5} - 28 q^{6} - 6 q^{7} - 8 q^{9} + O(q^{10}) \) \( 3840 q - 20 q^{3} + 1888 q^{4} - 10 q^{5} - 28 q^{6} - 6 q^{7} - 8 q^{9} - 48 q^{10} - 10 q^{11} - 10 q^{12} - 6 q^{13} - 26 q^{14} - 20 q^{15} - 1856 q^{16} - 32 q^{17} - 40 q^{18} - 84 q^{19} + 90 q^{20} + 52 q^{21} - 46 q^{22} - 2 q^{23} + 48 q^{24} - 470 q^{25} - 64 q^{26} - 20 q^{27} + 16 q^{28} - 10 q^{29} - 16 q^{31} + 42 q^{33} - 34 q^{34} + 84 q^{35} - 76 q^{36} - 36 q^{37} + 8 q^{38} - 4 q^{39} - 24 q^{40} - 10 q^{41} - 10 q^{42} - 10 q^{43} - 12 q^{44} - 20 q^{45} + 8 q^{46} - 10 q^{47} + 150 q^{48} - 70 q^{49} - 180 q^{50} - 26 q^{51} + 64 q^{52} - 40 q^{53} + 28 q^{54} + 12 q^{55} + 136 q^{56} - 76 q^{57} - 66 q^{58} - 10 q^{59} - 10 q^{61} + 20 q^{62} + 188 q^{63} - 3568 q^{64} + 38 q^{65} + 112 q^{66} + 20 q^{67} - 20 q^{68} + 22 q^{69} + 42 q^{70} - 20 q^{71} + 110 q^{72} + 32 q^{73} + 8 q^{74} + 110 q^{75} - 164 q^{76} - 90 q^{77} - 212 q^{78} - 70 q^{79} + 420 q^{80} - 96 q^{81} - 72 q^{82} + 54 q^{83} + 176 q^{84} - 42 q^{85} - 102 q^{86} - 44 q^{87} + 154 q^{88} - 156 q^{89} + 120 q^{90} + 32 q^{91} + 106 q^{92} - 2 q^{93} - 30 q^{94} + 86 q^{95} - 50 q^{96} + 24 q^{98} - 168 q^{99} + O(q^{100}) \)

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.