Properties

Label 2009.2.bt
Level $2009$
Weight $2$
Character orbit 2009.bt
Rep. character $\chi_{2009}(64,\cdot)$
Character field $\Q(\zeta_{70})$
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.bt (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{70})\)
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

\( 4656q - 15q^{2} + 177q^{4} - 11q^{5} - 45q^{6} - 30q^{7} - 11q^{8} + 740q^{9} + O(q^{10}) \) \( 4656q - 15q^{2} + 177q^{4} - 11q^{5} - 45q^{6} - 30q^{7} - 11q^{8} + 740q^{9} - 45q^{10} - 25q^{11} - 55q^{12} - 25q^{13} - 55q^{15} + 165q^{16} - 25q^{17} - 42q^{18} - 60q^{19} - 9q^{20} - 34q^{21} - 25q^{22} + 30q^{23} - 115q^{24} + 171q^{25} - 25q^{26} - 15q^{28} - 195q^{29} - 70q^{30} + 28q^{31} - 144q^{32} + 23q^{33} - 85q^{34} - 65q^{35} - 173q^{36} + 27q^{37} - 13q^{39} + 28q^{40} - 20q^{41} - 196q^{42} - 15q^{43} + 11q^{45} - 65q^{46} - 100q^{47} - 90q^{48} - 102q^{49} - 176q^{50} + 45q^{51} - 125q^{52} + 100q^{53} + 110q^{54} + 200q^{56} + 44q^{57} - 25q^{58} - 31q^{59} + 65q^{60} - 15q^{61} + 3q^{62} - 50q^{63} + 101q^{64} - 115q^{65} + 91q^{66} - 140q^{67} - 35q^{69} - 400q^{70} - 120q^{71} + 221q^{72} - 42q^{73} - 47q^{74} - 95q^{75} - 420q^{76} - 45q^{77} + 91q^{78} - 108q^{80} - 636q^{81} - 13q^{82} - 24q^{83} + 219q^{84} - 173q^{86} + 107q^{87} + 110q^{88} - 245q^{89} + 276q^{90} + 402q^{91} - 37q^{92} + 50q^{93} + 335q^{94} - 145q^{95} - 20q^{97} + 85q^{98} + O(q^{100}) \)

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

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