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Properties

Label 2001.2.bd
Level $2001$
Weight $2$
Character orbit 2001.bd
Rep. character $\chi_{2001}(160,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1440$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bd (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2928 1440 1488
Cusp forms 2832 1440 1392
Eisenstein series 96 0 96

Trace form

\( 1440 q - 8 q^{2} + 8 q^{8} + O(q^{10}) \) \( 1440 q - 8 q^{2} + 8 q^{8} + 224 q^{16} + 8 q^{18} + 4 q^{23} - 320 q^{25} + 24 q^{26} + 56 q^{29} + 48 q^{31} - 256 q^{32} + 112 q^{35} + 240 q^{36} + 16 q^{39} - 8 q^{41} + 48 q^{46} - 88 q^{47} + 224 q^{48} + 336 q^{49} - 16 q^{50} - 224 q^{52} + 56 q^{55} - 24 q^{58} - 16 q^{59} + 56 q^{69} - 152 q^{70} + 112 q^{71} + 64 q^{72} - 40 q^{73} + 16 q^{75} - 56 q^{77} + 240 q^{81} + 48 q^{82} - 128 q^{85} + 8 q^{87} - 32 q^{94} - 16 q^{95} - 144 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 2}\)