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Properties

Label 2169.2.bh
Level $2169$
Weight $2$
Character orbit 2169.bh
Rep. character $\chi_{2169}(4,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $960$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2169 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 976 976 0
Cusp forms 960 960 0
Eisenstein series 16 16 0

Trace form

\( 960 q - 6 q^{2} - 6 q^{3} + 478 q^{4} - 4 q^{7} + 18 q^{9} + O(q^{10}) \) \( 960 q - 6 q^{2} - 6 q^{3} + 478 q^{4} - 4 q^{7} + 18 q^{9} - 8 q^{10} - 6 q^{12} + 2 q^{13} - 24 q^{14} - 14 q^{15} - 470 q^{16} - 8 q^{17} - 6 q^{18} - 4 q^{19} + 12 q^{21} - 4 q^{22} - 8 q^{23} + 36 q^{24} + 460 q^{25} - 4 q^{26} + 18 q^{27} - 4 q^{28} + 12 q^{29} + 36 q^{30} + 6 q^{31} + 18 q^{32} + 58 q^{33} - 28 q^{34} - 4 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} - 16 q^{39} + 32 q^{40} - 68 q^{42} + 18 q^{43} - 18 q^{44} - 36 q^{45} + 8 q^{46} + 30 q^{48} - 72 q^{51} + 14 q^{52} - 12 q^{53} - 62 q^{54} - 16 q^{55} - 48 q^{56} + 56 q^{57} - 2 q^{58} + 48 q^{60} + 36 q^{61} + 38 q^{62} + 64 q^{63} - 976 q^{64} - 48 q^{65} + 8 q^{66} - 16 q^{68} + 42 q^{69} - 2 q^{70} - 20 q^{71} - 18 q^{72} - 18 q^{73} - 10 q^{74} + 12 q^{75} + 2 q^{76} + 90 q^{77} - 64 q^{78} + 36 q^{79} + 66 q^{80} - 86 q^{81} - 2 q^{82} - 30 q^{83} + 46 q^{84} + 32 q^{85} - 56 q^{86} - 4 q^{87} + 58 q^{88} - 4 q^{89} + 110 q^{90} + 12 q^{91} + 14 q^{92} - 6 q^{93} - 20 q^{94} - 8 q^{95} + 174 q^{96} + 80 q^{97} - 80 q^{98} - 74 q^{99} + O(q^{100}) \)

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.