Properties

Label 2009.2.c
Level 2009
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(2009, [\chi])\) into irreducible Hecke orbits

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

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