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Properties

Label 2009.2.bj
Level $2009$
Weight $2$
Character orbit 2009.bj
Rep. character $\chi_{2009}(48,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $2176$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bj (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 3264 2304 960
Cusp forms 3008 2176 832
Eisenstein series 256 128 128

Trace form

\( 2176 q + 32 q^{2} + 40 q^{4} - 48 q^{8} + 48 q^{9} + O(q^{10}) \) \( 2176 q + 32 q^{2} + 40 q^{4} - 48 q^{8} + 48 q^{9} + 32 q^{11} - 88 q^{15} + 520 q^{16} + 24 q^{18} - 48 q^{22} + 40 q^{23} + 40 q^{25} - 64 q^{29} - 48 q^{30} - 24 q^{32} - 48 q^{37} + 32 q^{39} - 112 q^{43} - 224 q^{44} - 112 q^{46} - 56 q^{50} - 48 q^{51} + 48 q^{53} - 64 q^{57} + 24 q^{58} + 192 q^{60} - 80 q^{64} + 40 q^{65} + 112 q^{67} - 176 q^{71} + 40 q^{72} + 120 q^{74} - 256 q^{78} + 40 q^{79} + 96 q^{85} + 40 q^{86} - 24 q^{88} + 128 q^{92} + 48 q^{93} + 32 q^{95} + 112 q^{99} + O(q^{100}) \)

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

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