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Properties

Label 2001.2.z
Level $2001$
Weight $2$
Character orbit 2001.z
Rep. character $\chi_{2001}(320,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.z (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2440 2240 200
Cusp forms 2360 2240 120
Eisenstein series 80 0 80

Trace form

\( 2240 q + 4 q^{3} + 216 q^{4} - 4 q^{9} + O(q^{10}) \) \( 2240 q + 4 q^{3} + 216 q^{4} - 4 q^{9} - 16 q^{12} - 22 q^{15} - 216 q^{16} - 56 q^{18} - 264 q^{25} + 16 q^{27} - 88 q^{30} - 8 q^{31} - 22 q^{33} - 44 q^{34} - 24 q^{36} - 88 q^{37} - 32 q^{39} - 308 q^{40} - 12 q^{46} + 132 q^{48} + 240 q^{49} - 180 q^{52} + 52 q^{54} + 72 q^{55} + 220 q^{60} + 88 q^{61} + 328 q^{64} + 122 q^{69} + 136 q^{70} + 172 q^{72} + 48 q^{73} + 78 q^{75} + 176 q^{76} - 324 q^{78} + 88 q^{79} - 140 q^{81} + 120 q^{82} - 308 q^{84} + 48 q^{85} - 418 q^{90} - 16 q^{93} - 168 q^{94} - 394 q^{96} - 132 q^{97} + O(q^{100}) \)

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

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