Properties

Label 2001.2.bu
Level $2001$
Weight $2$
Character orbit 2001.bu
Rep. character $\chi_{2001}(10,\cdot)$
Character field $\Q(\zeta_{308})$
Dimension $14400$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bu (of order \(308\) and degree \(120\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{308})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 29280 14400 14880
Cusp forms 28320 14400 13920
Eisenstein series 960 0 960

Trace form

\( 14400q + 8q^{2} - 8q^{8} + O(q^{10}) \) \( 14400q + 8q^{2} - 8q^{8} - 224q^{16} - 8q^{18} - 44q^{19} - 4q^{23} - 120q^{25} - 112q^{26} - 100q^{29} - 48q^{31} + 168q^{32} - 112q^{35} - 240q^{36} + 72q^{39} + 8q^{41} - 88q^{43} - 308q^{44} + 128q^{46} + 88q^{47} - 48q^{48} - 336q^{49} - 292q^{50} - 616q^{51} + 224q^{52} + 76q^{55} - 220q^{56} + 68q^{58} + 16q^{59} - 56q^{69} + 152q^{70} - 112q^{71} - 64q^{72} - 4q^{73} - 220q^{74} - 16q^{75} - 120q^{77} - 240q^{81} - 48q^{82} + 84q^{85} - 8q^{87} + 704q^{88} - 264q^{89} + 32q^{94} - 336q^{95} - 264q^{97} + 672q^{98} + O(q^{100}) \)

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

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