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 $392$

Related objects

Downloads

Learn more about

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

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

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

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