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Properties

Label 2009.2.u
Level $2009$
Weight $2$
Character orbit 2009.u
Rep. character $\chi_{2009}(204,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1164$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.u (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 1188 1188 0
Cusp forms 1164 1164 0
Eisenstein series 24 24 0

Trace form

\( 1164 q - 10 q^{2} - 202 q^{4} - 14 q^{5} - 14 q^{8} + 160 q^{9} + O(q^{10}) \) \( 1164 q - 10 q^{2} - 202 q^{4} - 14 q^{5} - 14 q^{8} + 160 q^{9} - 10 q^{10} - 190 q^{16} - 28 q^{18} + 14 q^{20} - 26 q^{21} + 20 q^{23} - 196 q^{25} - 88 q^{31} + 94 q^{32} + 2 q^{33} + 58 q^{36} + 18 q^{37} - 42 q^{39} - 18 q^{40} + 25 q^{41} - 134 q^{42} - 10 q^{43} - 16 q^{45} + 70 q^{46} + 52 q^{49} - 24 q^{50} + 30 q^{51} + 6 q^{57} + 6 q^{59} - 30 q^{61} - 98 q^{62} - 226 q^{64} - 46 q^{66} - 196 q^{72} - 48 q^{73} + 22 q^{74} + 20 q^{77} - 146 q^{78} + 128 q^{80} - 364 q^{81} + 68 q^{82} + 134 q^{83} + 196 q^{84} + 128 q^{86} - 162 q^{87} + 14 q^{90} - 262 q^{91} + 102 q^{92} + 40 q^{98} + O(q^{100}) \)

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.