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Properties

Label 2009.2.j
Level $2009$
Weight $2$
Character orbit 2009.j
Rep. character $\chi_{2009}(655,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $272$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 408 288 120
Cusp forms 376 272 104
Eisenstein series 32 16 16

Trace form

\( 272 q + 2 q^{2} - 130 q^{4} + 6 q^{5} - 12 q^{8} + 134 q^{9} + O(q^{10}) \) \( 272 q + 2 q^{2} - 130 q^{4} + 6 q^{5} - 12 q^{8} + 134 q^{9} - 16 q^{10} - 118 q^{16} + 12 q^{18} - 16 q^{20} + 4 q^{23} - 94 q^{25} - 6 q^{31} - 16 q^{32} + 20 q^{33} - 324 q^{36} + 32 q^{37} - 14 q^{39} - 44 q^{40} - 24 q^{41} + 32 q^{43} - 26 q^{45} + 12 q^{46} - 144 q^{50} - 24 q^{51} - 32 q^{57} - 2 q^{59} - 14 q^{61} + 20 q^{62} + 236 q^{64} + 4 q^{66} + 60 q^{72} + 16 q^{73} + 20 q^{74} + 12 q^{78} + 52 q^{80} - 44 q^{81} + 42 q^{82} + 112 q^{83} - 12 q^{86} + 18 q^{87} - 224 q^{90} + 4 q^{92} + O(q^{100}) \)

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

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