↑

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 $392$

Related objects

Downloads

Learn more

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

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

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.