Properties

Label 2001.2.bh
Level $2001$
Weight $2$
Character orbit 2001.bh
Rep. character $\chi_{2001}(157,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2400$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bh (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 4880 2400 2480
Cusp forms 4720 2400 2320
Eisenstein series 160 0 160

Trace form

\( 2400q - 8q^{2} + 8q^{8} + O(q^{10}) \) \( 2400q - 8q^{2} + 8q^{8} + 224q^{16} + 8q^{18} + 44q^{19} - 24q^{23} - 384q^{25} + 112q^{26} + 44q^{29} - 8q^{31} + 56q^{32} + 240q^{36} - 72q^{39} - 8q^{41} + 88q^{43} + 308q^{44} - 156q^{46} + 24q^{47} - 176q^{48} + 224q^{49} + 292q^{50} - 76q^{55} + 220q^{56} - 68q^{58} - 16q^{59} + 72q^{70} + 8q^{72} + 4q^{73} - 88q^{74} + 16q^{75} + 120q^{77} + 240q^{81} + 48q^{82} + 84q^{85} + 8q^{87} - 704q^{88} + 264q^{89} - 32q^{94} + 336q^{95} + 264q^{97} - 392q^{98} + O(q^{100}) \)

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

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