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

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

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

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