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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

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

Display 100 coefficients 10 coefficients

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

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