Properties

Label 2009.2.bw
Level $2009$
Weight $2$
Character orbit 2009.bw
Rep. character $\chi_{2009}(16,\cdot)$
Character field $\Q(\zeta_{105})$
Dimension $9312$
Sturm bound $392$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bw (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{105})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 9504 9504 0
Cusp forms 9312 9312 0
Eisenstein series 192 192 0

Trace form

\( 9312q - 39q^{2} - 104q^{3} - 231q^{4} - 35q^{5} - 62q^{6} - 36q^{7} - 10q^{8} + 624q^{9} + O(q^{10}) \) \( 9312q - 39q^{2} - 104q^{3} - 231q^{4} - 35q^{5} - 62q^{6} - 36q^{7} - 10q^{8} + 624q^{9} - 18q^{10} - 43q^{11} - 61q^{12} - 30q^{13} - 50q^{14} - 36q^{15} - 231q^{16} - 45q^{17} - 21q^{18} - 22q^{19} + 6q^{20} - 62q^{21} + 2q^{22} + 33q^{23} - 108q^{24} - 225q^{25} - 85q^{26} - 182q^{27} - 115q^{28} + 48q^{29} - 44q^{30} - 94q^{31} - 210q^{32} - 52q^{33} + 66q^{34} - 40q^{35} + 156q^{36} - 18q^{37} - 130q^{38} - 40q^{39} - 182q^{40} - 22q^{41} + 200q^{42} - 30q^{43} - 716q^{44} - 180q^{45} + 176q^{46} + 46q^{47} - 194q^{48} + 60q^{49} - 216q^{50} - 204q^{51} - 111q^{52} + 133q^{53} + 146q^{54} - 74q^{55} - 444q^{56} + q^{57} + 47q^{58} - 55q^{59} - 258q^{60} - 33q^{61} - 100q^{62} - 96q^{63} + 298q^{64} - 48q^{65} + 384q^{66} - 10q^{67} - 14q^{68} - 88q^{69} + 347q^{70} + 47q^{71} - 329q^{72} - 184q^{73} - 121q^{74} - 262q^{75} + 99q^{76} - 28q^{77} - 132q^{78} - 62q^{79} - 158q^{80} + 396q^{81} - 35q^{82} - 44q^{83} + 243q^{84} - 52q^{85} + 45q^{86} + 172q^{87} - 492q^{88} - 233q^{89} - 291q^{90} - 662q^{91} - 112q^{92} - 112q^{93} + 241q^{94} - 65q^{95} + 680q^{96} - 228q^{97} - 5q^{98} - 56q^{99} + O(q^{100}) \)

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

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