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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

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

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

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