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

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

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

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

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

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