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Properties

Label 2009.2.bd
Level $2009$
Weight $2$
Character orbit 2009.bd
Rep. character $\chi_{2009}(155,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2328$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bd (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 2376 2376 0
Cusp forms 2328 2328 0
Eisenstein series 48 48 0

Trace form

\( 2328 q - 10 q^{3} + 364 q^{4} + 2 q^{6} - 12 q^{7} + O(q^{10}) \) \( 2328 q - 10 q^{3} + 364 q^{4} + 2 q^{6} - 12 q^{7} - 44 q^{10} - 18 q^{11} - 6 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} - 412 q^{16} + 2 q^{17} - 64 q^{18} - 16 q^{19} + 6 q^{22} - 20 q^{23} - 50 q^{24} + 352 q^{25} - 58 q^{26} - 4 q^{27} + 48 q^{28} + 58 q^{29} - 32 q^{30} - 208 q^{31} - 58 q^{34} - 52 q^{35} - 28 q^{37} + 82 q^{38} - 20 q^{40} - 58 q^{41} - 264 q^{42} - 62 q^{44} + 44 q^{45} - 84 q^{47} + 12 q^{48} + 4 q^{51} + 62 q^{52} + 20 q^{53} + 52 q^{54} + 16 q^{55} - 94 q^{56} - 48 q^{57} + 50 q^{58} - 28 q^{59} + 70 q^{60} + 26 q^{63} + 332 q^{64} + 34 q^{65} + 164 q^{66} - 40 q^{67} - 28 q^{68} - 58 q^{69} - 116 q^{70} + 48 q^{71} + 120 q^{72} - 114 q^{75} - 212 q^{76} + 212 q^{78} + 4 q^{79} + 56 q^{81} - 2 q^{82} - 28 q^{83} - 22 q^{85} - 52 q^{86} - 240 q^{88} - 118 q^{89} - 76 q^{92} - 98 q^{93} - 176 q^{94} - 32 q^{95} + 166 q^{96} - 140 q^{97} - 24 q^{98} - 80 q^{99} + O(q^{100}) \)

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.