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Properties

Label 2009.2.bo
Level $2009$
Weight $2$
Character orbit 2009.bo
Rep. character $\chi_{2009}(27,\cdot)$
Character field $\Q(\zeta_{56})$
Dimension $4656$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bo (of order \(56\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{56})\)
Sturm bound: \(392\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2009, [\chi])\).

Total New Old
Modular forms 4752 4752 0
Cusp forms 4656 4656 0
Eisenstein series 96 96 0

Trace form

\( 4656 q - 20 q^{2} - 28 q^{3} - 28 q^{5} - 28 q^{6} - 24 q^{7} - 36 q^{8} + 20 q^{9} + O(q^{10}) \) \( 4656 q - 20 q^{2} - 28 q^{3} - 28 q^{5} - 28 q^{6} - 24 q^{7} - 36 q^{8} + 20 q^{9} - 56 q^{10} - 20 q^{11} - 28 q^{12} - 28 q^{13} - 20 q^{14} + 4 q^{15} + 712 q^{16} - 28 q^{17} - 96 q^{18} - 28 q^{20} - 4 q^{21} - 68 q^{22} + 140 q^{24} + 28 q^{26} - 28 q^{27} - 40 q^{28} - 4 q^{29} - 88 q^{30} + 4 q^{32} - 28 q^{33} - 28 q^{34} - 40 q^{35} + 28 q^{36} - 88 q^{37} - 28 q^{38} - 20 q^{39} - 28 q^{41} - 48 q^{42} - 20 q^{43} + 68 q^{44} + 44 q^{46} - 56 q^{47} - 16 q^{49} - 104 q^{50} - 88 q^{51} - 28 q^{52} - 60 q^{53} - 112 q^{54} - 28 q^{55} + 148 q^{56} + 144 q^{57} + 36 q^{58} - 56 q^{59} - 100 q^{60} - 28 q^{61} - 84 q^{62} + 104 q^{63} - 76 q^{65} - 96 q^{67} - 28 q^{69} + 104 q^{70} + 60 q^{71} + 56 q^{73} - 60 q^{74} - 364 q^{75} - 560 q^{76} - 12 q^{77} + 56 q^{78} - 56 q^{79} - 28 q^{82} - 56 q^{83} + 96 q^{84} - 4 q^{85} - 252 q^{87} - 272 q^{88} + 168 q^{89} - 168 q^{90} - 92 q^{91} - 104 q^{92} - 244 q^{93} + 560 q^{94} - 20 q^{95} - 28 q^{96} - 48 q^{98} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2009, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.