Properties

Label 2001.2.d
Level $2001$
Weight $2$
Character orbit 2001.d
Rep. character $\chi_{2001}(1103,\cdot)$
Character field $\Q$
Dimension $224$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2001, [\chi])\).

Total New Old
Modular forms 244 224 20
Cusp forms 236 224 12
Eisenstein series 8 0 8

Trace form

\( 224q - 4q^{3} - 216q^{4} + 4q^{9} + O(q^{10}) \) \( 224q - 4q^{3} - 216q^{4} + 4q^{9} + 16q^{12} + 216q^{16} - 32q^{18} + 264q^{25} - 16q^{27} + 8q^{31} + 24q^{36} + 32q^{39} + 12q^{46} - 132q^{48} - 240q^{49} - 40q^{52} - 52q^{54} - 72q^{55} - 152q^{64} - 12q^{69} + 40q^{70} + 92q^{72} - 48q^{73} - 12q^{75} + 104q^{78} - 36q^{81} - 120q^{82} - 48q^{85} + 16q^{93} + 168q^{94} - 24q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2001, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)