Properties

Label 2009.2.bh
Level $2009$
Weight $2$
Character orbit 2009.bh
Rep. character $\chi_{2009}(57,\cdot)$
Character field $\Q(\zeta_{35})$
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.bh (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{35})\)
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

\( 4656q - 15q^{2} - 40q^{3} + 177q^{4} - 19q^{5} + 17q^{6} - 18q^{7} - 35q^{8} - 780q^{9} + O(q^{10}) \) \( 4656q - 15q^{2} - 40q^{3} + 177q^{4} - 19q^{5} + 17q^{6} - 18q^{7} - 35q^{8} - 780q^{9} - 9q^{10} - 23q^{11} - 5q^{12} - 15q^{13} - 46q^{14} - 9q^{15} + 165q^{16} - 27q^{17} - 6q^{18} - 44q^{19} - 33q^{20} - 22q^{21} - 47q^{22} - 60q^{23} + 75q^{24} + 171q^{25} - 23q^{26} + 26q^{27} + 61q^{28} - 93q^{29} - 34q^{30} + 28q^{31} - 24q^{32} + 43q^{33} - 3q^{34} + 13q^{35} + 351q^{36} + 27q^{37} - 92q^{38} - 17q^{39} - 100q^{40} - 8q^{41} - 236q^{42} - 15q^{43} - 304q^{44} + 75q^{45} + 139q^{46} - 64q^{47} - 106q^{48} + 30q^{49} - 72q^{50} - 39q^{51} - 3q^{52} - 70q^{53} + 4q^{54} - 46q^{55} - 18q^{56} - 46q^{57} - 11q^{58} - 107q^{59} + 135q^{60} + 33q^{61} + 7q^{62} - 18q^{63} + 197q^{64} - 33q^{65} - 501q^{66} - 20q^{67} - 160q^{68} - 29q^{69} - 212q^{70} - 92q^{71} + 209q^{72} + 22q^{73} - 119q^{74} + 223q^{75} - 288q^{76} + 19q^{77} + 15q^{78} - 124q^{79} + 140q^{80} - 588q^{81} + 125q^{82} + 176q^{83} - 243q^{84} - 68q^{85} + 111q^{86} - q^{87} - 192q^{88} + 77q^{89} + 66q^{90} + 146q^{91} + 67q^{92} - 2q^{93} - 49q^{94} + 83q^{95} - 476q^{96} + 120q^{97} - 103q^{98} - 52q^{99} + O(q^{100}) \)

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

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