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Properties

Label 2009.2.c
Level $2009$
Weight $2$
Character orbit 2009.c
Rep. character $\chi_{2009}(491,\cdot)$
Character field $\Q$
Dimension $138$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 204 148 56
Cusp forms 188 138 50
Eisenstein series 16 10 6

Trace form

\( 138 q + 2 q^{2} + 134 q^{4} + 4 q^{5} - 6 q^{8} - 126 q^{9} + O(q^{10}) \) \( 138 q + 2 q^{2} + 134 q^{4} + 4 q^{5} - 6 q^{8} - 126 q^{9} + 134 q^{16} - 14 q^{18} + 24 q^{20} - 16 q^{23} + 98 q^{25} + 8 q^{31} + 30 q^{32} - 158 q^{36} + 20 q^{37} + 4 q^{39} + 8 q^{40} + 12 q^{41} + 24 q^{43} - 36 q^{45} - 24 q^{46} - 70 q^{50} + 24 q^{51} - 8 q^{57} + 28 q^{59} - 20 q^{61} - 40 q^{62} + 78 q^{64} - 72 q^{66} + 30 q^{72} + 36 q^{73} - 24 q^{74} + 16 q^{78} + 40 q^{80} + 82 q^{81} - 24 q^{82} - 16 q^{83} - 56 q^{86} - 4 q^{87} + 76 q^{90} - 40 q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)