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Properties

Label 2169.2.bl
Level $2169$
Weight $2$
Character orbit 2169.bl
Rep. character $\chi_{2169}(205,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1920$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.bl (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2169 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1920 q - 8 q^{3} - 960 q^{4} - 7 q^{5} + 6 q^{6} - 5 q^{7} - 48 q^{8} - 16 q^{9} + O(q^{10}) \) \( 1920 q - 8 q^{3} - 960 q^{4} - 7 q^{5} + 6 q^{6} - 5 q^{7} - 48 q^{8} - 16 q^{9} - 6 q^{11} + 11 q^{12} + 13 q^{14} - 28 q^{15} - 960 q^{16} - 36 q^{17} - 6 q^{18} + 20 q^{19} + 3 q^{20} - 42 q^{21} + 30 q^{22} + 3 q^{23} - 54 q^{24} + 229 q^{25} + 13 q^{27} + 40 q^{28} + 3 q^{29} - 34 q^{30} - 11 q^{31} + 48 q^{32} - 81 q^{33} + 15 q^{34} - 68 q^{35} - 58 q^{36} - 8 q^{37} - 18 q^{39} - 30 q^{40} + 17 q^{41} - 76 q^{42} + 15 q^{43} + 52 q^{44} - 10 q^{45} + 60 q^{46} - 5 q^{47} - 30 q^{48} + 205 q^{49} - 58 q^{50} - 6 q^{51} + 27 q^{52} + 12 q^{53} + 23 q^{54} + 42 q^{55} - 44 q^{56} - 72 q^{57} + 27 q^{58} - 13 q^{59} + 150 q^{60} - 5 q^{61} + 66 q^{62} - 192 q^{63} + 1896 q^{64} - 2 q^{65} + 130 q^{66} - 26 q^{67} - 32 q^{68} + 17 q^{69} - 45 q^{70} - 24 q^{71} + 73 q^{72} - 20 q^{73} - 9 q^{74} + 70 q^{75} - 100 q^{76} + 6 q^{77} - 140 q^{78} + 18 q^{79} + 134 q^{80} - 104 q^{81} + 36 q^{82} - 90 q^{83} + 128 q^{84} - 17 q^{85} + 107 q^{86} - 88 q^{87} - 6 q^{88} - 108 q^{89} + 69 q^{90} + 4 q^{91} + 97 q^{92} - 48 q^{93} + 21 q^{94} - 6 q^{95} + 55 q^{96} - 56 q^{97} + 8 q^{98} + 76 q^{99} + O(q^{100}) \)

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.