↑

Properties

Label 2001.2.bo
Level $2001$
Weight $2$
Character orbit 2001.bo
Rep. character $\chi_{2001}(4,\cdot)$
Character field $\Q(\zeta_{154})$
Dimension $7200$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bo (of order \(154\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{154})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 14640 7200 7440
Cusp forms 14160 7200 6960
Eisenstein series 480 0 480

Trace form

\( 7200 q - 112 q^{4} - 8 q^{7} - 120 q^{9} + O(q^{10}) \) \( 7200 q - 112 q^{4} - 8 q^{7} - 120 q^{9} + 56 q^{11} + 20 q^{13} - 52 q^{16} - 52 q^{22} + 70 q^{23} + 292 q^{25} - 112 q^{28} - 50 q^{29} + 80 q^{30} - 28 q^{31} + 28 q^{32} + 16 q^{33} - 16 q^{34} + 32 q^{35} + 156 q^{36} - 28 q^{37} - 228 q^{38} - 8 q^{42} + 28 q^{43} - 28 q^{44} - 56 q^{47} - 112 q^{48} + 88 q^{49} + 112 q^{50} + 196 q^{51} + 132 q^{52} + 16 q^{53} - 252 q^{55} + 196 q^{56} - 48 q^{57} + 46 q^{58} - 32 q^{59} - 56 q^{61} + 180 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{65} - 112 q^{66} - 108 q^{67} - 28 q^{69} + 76 q^{71} - 28 q^{72} + 98 q^{74} - 112 q^{76} - 16 q^{78} + 28 q^{79} + 348 q^{80} + 120 q^{81} - 24 q^{82} + 152 q^{83} - 28 q^{85} - 1152 q^{86} + 88 q^{87} - 184 q^{88} + 28 q^{89} - 340 q^{91} + 58 q^{92} + 32 q^{93} - 48 q^{94} - 28 q^{97} - 140 q^{98} + O(q^{100}) \)

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

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