Properties

Label 2009.2.m
Level $2009$
Weight $2$
Character orbit 2009.m
Rep. character $\chi_{2009}(342,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $544$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 816 576 240
Cusp forms 752 544 208
Eisenstein series 64 32 32

Trace form

\( 544q + 8q^{2} - 32q^{8} - 8q^{9} + O(q^{10}) \) \( 544q + 8q^{2} - 32q^{8} - 8q^{9} + 8q^{11} + 8q^{15} - 480q^{16} + 16q^{18} - 32q^{22} - 16q^{29} + 8q^{30} + 64q^{32} - 80q^{36} - 32q^{37} + 8q^{39} + 32q^{43} + 24q^{44} + 152q^{46} - 24q^{50} - 32q^{51} - 8q^{53} - 16q^{57} + 16q^{58} - 152q^{60} - 72q^{67} + 96q^{71} - 80q^{74} + 176q^{78} - 176q^{85} + 64q^{88} - 208q^{92} - 8q^{93} + 8q^{95} - 192q^{99} + O(q^{100}) \)

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

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