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Properties

Label 2009.2.bg
Level $2009$
Weight $2$
Character orbit 2009.bg
Rep. character $\chi_{2009}(312,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1088$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 1632 1152 480
Cusp forms 1504 1088 416
Eisenstein series 128 64 64

Trace form

\( 1088 q + 3 q^{2} + 135 q^{4} - q^{5} + 40 q^{6} - 28 q^{8} + 516 q^{9} + O(q^{10}) \) \( 1088 q + 3 q^{2} + 135 q^{4} - q^{5} + 40 q^{6} - 28 q^{8} + 516 q^{9} + 6 q^{10} + 5 q^{11} + 35 q^{12} + 20 q^{13} - 10 q^{15} + 123 q^{16} + 5 q^{17} + 18 q^{18} + 5 q^{19} + 96 q^{20} - 120 q^{22} + 6 q^{23} - 40 q^{24} + 99 q^{25} + 5 q^{26} - 80 q^{29} - 45 q^{30} + 11 q^{31} + 26 q^{32} + 10 q^{33} - 100 q^{34} + 374 q^{36} + 8 q^{37} + 4 q^{39} - 6 q^{40} + 14 q^{41} - 32 q^{43} - 34 q^{45} + 8 q^{46} - 25 q^{47} + 50 q^{48} + 144 q^{50} - 76 q^{51} + 105 q^{52} - 20 q^{53} + 35 q^{54} + 102 q^{57} + 5 q^{58} + 37 q^{59} + 150 q^{60} - 51 q^{61} + 70 q^{62} - 176 q^{64} - 40 q^{65} + 176 q^{66} + 5 q^{67} + 30 q^{69} - 50 q^{71} - 75 q^{72} + 34 q^{73} - 75 q^{74} + 120 q^{75} - 110 q^{76} - 262 q^{78} - 127 q^{80} - 416 q^{81} + 63 q^{82} + 128 q^{83} + 107 q^{86} - 28 q^{87} - 270 q^{88} - 35 q^{89} + 34 q^{90} - 134 q^{92} - 15 q^{93} + 155 q^{94} - 55 q^{95} - 20 q^{97} - 260 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2009, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)