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Properties

Label 2169.2.dh
Level $2169$
Weight $2$
Character orbit 2169.dh
Rep. character $\chi_{2169}(67,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $7680$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.dh (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2169 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 7808 7808 0
Cusp forms 7680 7680 0
Eisenstein series 128 128 0

Trace form

\( 7680 q - 16 q^{2} - 32 q^{3} - 16 q^{5} - 40 q^{6} - 16 q^{7} - 32 q^{8} - 28 q^{9} + O(q^{10}) \) \( 7680 q - 16 q^{2} - 32 q^{3} - 16 q^{5} - 40 q^{6} - 16 q^{7} - 32 q^{8} - 28 q^{9} - 72 q^{10} - 16 q^{11} + 92 q^{12} - 16 q^{13} - 20 q^{14} - 16 q^{15} - 7520 q^{16} - 88 q^{17} - 48 q^{18} - 64 q^{19} + 248 q^{20} - 40 q^{21} - 16 q^{22} - 28 q^{23} + 108 q^{24} - 20 q^{25} - 64 q^{26} - 20 q^{27} - 16 q^{28} - 28 q^{29} + 96 q^{30} - 32 q^{31} - 80 q^{32} + 20 q^{33} + 8 q^{34} - 64 q^{35} + 64 q^{36} - 64 q^{37} + 32 q^{38} - 32 q^{39} + 12 q^{40} - 8 q^{41} - 8 q^{42} - 36 q^{43} - 12 q^{44} - 24 q^{45} - 160 q^{46} - 16 q^{47} + 24 q^{48} + 180 q^{49} + 120 q^{50} - 72 q^{51} + 224 q^{52} - 64 q^{53} - 36 q^{54} - 88 q^{55} + 240 q^{56} + 68 q^{57} - 12 q^{58} - 72 q^{59} - 120 q^{60} + 8 q^{61} - 64 q^{62} - 32 q^{63} + 64 q^{65} - 204 q^{66} - 28 q^{67} + 124 q^{68} - 84 q^{69} - 36 q^{70} - 64 q^{71} + 20 q^{72} - 8 q^{73} - 16 q^{74} + 76 q^{75} - 136 q^{76} - 112 q^{77} - 128 q^{78} - 64 q^{79} - 128 q^{80} - 92 q^{81} - 20 q^{82} - 20 q^{83} - 64 q^{84} - 112 q^{85} - 16 q^{86} - 44 q^{87} + 204 q^{88} - 112 q^{89} - 28 q^{90} + 8 q^{91} + 204 q^{92} - 116 q^{93} - 24 q^{94} - 272 q^{95} - 264 q^{96} - 152 q^{97} - 192 q^{98} - 104 q^{99} + O(q^{100}) \)

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.