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Properties

Label 2009.2.cd
Level $2009$
Weight $2$
Character orbit 2009.cd
Rep. character $\chi_{2009}(4,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $9312$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.cd (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{210})\)
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

\( 9312 q - 39 q^{2} - 231 q^{4} - 43 q^{5} - 30 q^{6} - 60 q^{7} - 34 q^{8} - 896 q^{9} + O(q^{10}) \) \( 9312 q - 39 q^{2} - 231 q^{4} - 43 q^{5} - 30 q^{6} - 60 q^{7} - 34 q^{8} - 896 q^{9} - 36 q^{10} - 65 q^{11} - 35 q^{12} - 50 q^{13} - 20 q^{15} - 231 q^{16} - 65 q^{17} - 39 q^{18} - 30 q^{19} + 54 q^{20} - 50 q^{21} - 50 q^{22} - 111 q^{23} - 110 q^{24} - 225 q^{25} - 65 q^{26} - 75 q^{28} + 120 q^{29} + 10 q^{30} - 94 q^{31} - 18 q^{32} - 32 q^{33} - 170 q^{34} - 70 q^{35} - 424 q^{36} - 18 q^{37} - 38 q^{39} - 118 q^{40} - 70 q^{41} + 232 q^{42} - 30 q^{43} - 62 q^{45} - 178 q^{46} + 10 q^{47} - 90 q^{48} - 168 q^{49} - 112 q^{50} + 144 q^{51} + 35 q^{52} - 265 q^{53} - 140 q^{54} + 250 q^{56} - 89 q^{57} - 65 q^{58} - 131 q^{59} - 20 q^{60} - 93 q^{61} - 40 q^{63} + 394 q^{64} - 110 q^{65} + 50 q^{66} - 70 q^{67} - 40 q^{69} + 175 q^{70} + 45 q^{71} - 269 q^{72} - 120 q^{73} - q^{74} + 50 q^{75} + 345 q^{76} - 72 q^{77} - 64 q^{78} + 90 q^{80} + 372 q^{81} + 7 q^{82} + 156 q^{83} - 327 q^{84} - 139 q^{86} + 154 q^{87} + 610 q^{88} - 385 q^{89} - 141 q^{90} - 210 q^{91} - 8 q^{92} - 140 q^{93} - 335 q^{94} - 125 q^{95} - 160 q^{97} - 193 q^{98} - 180 q^{99} + O(q^{100}) \)

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.