Properties

Label 2001.2.l
Level $2001$
Weight $2$
Character orbit 2001.l
Rep. character $\chi_{2001}(737,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $440$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 488 440 48
Cusp forms 472 440 32
Eisenstein series 16 0 16

Trace form

\( 440q + O(q^{10}) \) \( 440q + 24q^{10} + 6q^{12} - 20q^{15} - 440q^{16} - 34q^{18} - 20q^{21} + 24q^{24} + 440q^{25} + 24q^{27} + 32q^{30} - 12q^{36} + 56q^{37} - 52q^{39} - 72q^{40} - 8q^{43} + 64q^{45} - 22q^{48} + 392q^{49} + 24q^{52} - 24q^{54} - 64q^{55} - 28q^{58} + 48q^{60} - 72q^{61} - 28q^{66} - 48q^{70} + 84q^{72} + 16q^{73} - 100q^{75} + 88q^{76} + 40q^{78} - 120q^{79} + 48q^{81} - 96q^{82} + 36q^{84} - 48q^{85} + 44q^{87} - 128q^{88} + 104q^{90} + 224q^{94} + 120q^{97} - 28q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)