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Properties

Label 3009.2.bf
Level $3009$
Weight $2$
Character orbit 3009.bf
Rep. character $\chi_{3009}(38,\cdot)$
Character field $\Q(\zeta_{116})$
Dimension $19936$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.bf (of order \(116\) and degree \(56\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3009 \)
Character field: \(\Q(\zeta_{116})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 20384 20384 0
Cusp forms 19936 19936 0
Eisenstein series 448 448 0

Trace form

\( 19936 q - 58 q^{3} + 488 q^{4} - 58 q^{6} - 108 q^{7} + O(q^{10}) \) \( 19936 q - 58 q^{3} + 488 q^{4} - 58 q^{6} - 108 q^{7} - 116 q^{10} - 58 q^{12} - 232 q^{13} - 936 q^{16} - 116 q^{18} - 96 q^{21} - 100 q^{22} - 58 q^{24} - 40 q^{27} - 124 q^{28} - 116 q^{30} - 116 q^{31} - 116 q^{33} - 116 q^{34} - 116 q^{37} - 58 q^{39} - 116 q^{40} - 76 q^{45} - 92 q^{46} - 98 q^{48} - 66 q^{51} - 232 q^{52} + 348 q^{54} - 232 q^{55} - 92 q^{57} - 116 q^{61} - 78 q^{63} + 472 q^{64} - 232 q^{67} - 580 q^{69} - 116 q^{72} - 116 q^{73} - 78 q^{75} + 10 q^{78} - 156 q^{79} - 52 q^{81} - 116 q^{82} - 180 q^{84} - 100 q^{85} - 308 q^{88} - 58 q^{90} - 116 q^{91} - 58 q^{96} - 116 q^{97} - 58 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into newform subspaces

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