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Properties

Label 2169.2.bm
Level $2169$
Weight $2$
Character orbit 2169.bm
Rep. character $\chi_{2169}(265,\cdot)$
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.bm (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

\( 1920 q + 12 q^{2} - 5 q^{3} - 948 q^{4} - 7 q^{5} - 5 q^{7} - 96 q^{8} + 5 q^{9} + O(q^{10}) \) \( 1920 q + 12 q^{2} - 5 q^{3} - 948 q^{4} - 7 q^{5} - 5 q^{7} - 96 q^{8} + 5 q^{9} - 30 q^{10} + 3 q^{11} + 20 q^{12} - 5 q^{14} + 2 q^{15} - 924 q^{16} - 36 q^{17} - 15 q^{18} + 5 q^{19} + 57 q^{20} + 18 q^{21} + 33 q^{22} + 3 q^{23} - 45 q^{24} + 229 q^{25} - 18 q^{26} - 32 q^{27} - 38 q^{28} - 9 q^{29} - 40 q^{30} - 11 q^{31} + 138 q^{32} + 9 q^{33} + 54 q^{34} - 77 q^{35} - 46 q^{36} - 17 q^{37} - 12 q^{38} - 21 q^{39} + 30 q^{40} - 76 q^{41} + 23 q^{42} - 42 q^{43} - 74 q^{44} - 148 q^{45} - 42 q^{46} - 5 q^{47} - 159 q^{48} + 205 q^{49} + 56 q^{50} + 6 q^{51} - 30 q^{53} - q^{54} - 42 q^{55} - 14 q^{56} - 33 q^{57} - 48 q^{58} + 59 q^{59} - 3 q^{60} - 23 q^{61} + 105 q^{62} - 9 q^{63} + 1752 q^{64} - 2 q^{65} + 40 q^{66} + 43 q^{67} + 76 q^{68} + 71 q^{69} + 21 q^{70} - 21 q^{71} - 86 q^{72} + 34 q^{73} + 9 q^{74} - 131 q^{75} + 38 q^{76} + 75 q^{77} + 79 q^{78} - 51 q^{79} - 214 q^{80} + 13 q^{81} - 21 q^{82} - 9 q^{83} + 251 q^{84} + 19 q^{85} - q^{86} + 56 q^{87} + 99 q^{88} - 27 q^{89} + 78 q^{90} + 4 q^{91} - 71 q^{92} - 9 q^{93} + 21 q^{94} + 102 q^{95} - 26 q^{96} - 50 q^{97} + 32 q^{98} + 58 q^{99} + O(q^{100}) \)

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.