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Properties

Label 2169.2.e
Level $2169$
Weight $2$
Character orbit 2169.e
Rep. character $\chi_{2169}(256,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $480$
Sturm bound $484$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 488 488 0
Cusp forms 480 480 0
Eisenstein series 8 8 0

Trace form

\( 480 q + 3 q^{2} - 5 q^{3} - 237 q^{4} + 2 q^{5} - 24 q^{8} - 15 q^{9} + O(q^{10}) \) \( 480 q + 3 q^{2} - 5 q^{3} - 237 q^{4} + 2 q^{5} - 24 q^{8} - 15 q^{9} + 2 q^{11} - 5 q^{12} + 10 q^{14} - 7 q^{15} - 231 q^{16} + 16 q^{17} + 15 q^{18} - 2 q^{20} - 3 q^{21} + 12 q^{22} - 8 q^{23} - 15 q^{24} - 234 q^{25} - 12 q^{26} - 8 q^{27} - 12 q^{28} + 4 q^{29} + 10 q^{30} + 6 q^{31} - 3 q^{32} + q^{33} - 9 q^{34} - 3 q^{35} - 34 q^{36} - 3 q^{37} + 32 q^{38} + 11 q^{39} + 11 q^{41} + 42 q^{42} - 3 q^{43} - 26 q^{44} - 2 q^{45} - 18 q^{46} + 30 q^{47} + 4 q^{48} - 240 q^{49} - 106 q^{50} - q^{51} + 15 q^{52} + 10 q^{53} + 66 q^{54} - 3 q^{55} + 4 q^{56} - 22 q^{57} + 3 q^{58} - 64 q^{59} + 58 q^{60} + 18 q^{61} + 15 q^{62} - 46 q^{63} + 408 q^{64} - 8 q^{65} + 100 q^{66} - 18 q^{67} - 46 q^{68} - 16 q^{69} + 54 q^{70} + q^{71} + q^{72} - 54 q^{73} + 6 q^{74} - 4 q^{75} - 3 q^{76} + 55 q^{77} + 56 q^{78} - 9 q^{79} - 21 q^{80} - 63 q^{81} - 9 q^{82} - 16 q^{83} - 51 q^{84} - 24 q^{85} + 36 q^{86} - 6 q^{87} + 36 q^{88} + 17 q^{89} - 3 q^{90} - 24 q^{91} + 126 q^{92} - q^{93} - 6 q^{94} + 68 q^{95} + 61 q^{96} - 62 q^{98} + 27 q^{99} + O(q^{100}) \)

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.