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Properties

Label 2001.2.n
Level $2001$
Weight $2$
Character orbit 2001.n
Rep. character $\chi_{2001}(262,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1120$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.n (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2440 1120 1320
Cusp forms 2360 1120 1240
Eisenstein series 80 0 80

Trace form

\( 1120 q - 104 q^{4} + 8 q^{5} + 8 q^{6} + 8 q^{7} - 112 q^{9} + O(q^{10}) \) \( 1120 q - 104 q^{4} + 8 q^{5} + 8 q^{6} + 8 q^{7} - 112 q^{9} + 16 q^{10} + 32 q^{11} + 8 q^{13} + 16 q^{14} + 8 q^{15} - 88 q^{16} - 28 q^{17} + 48 q^{19} - 104 q^{20} + 8 q^{21} + 56 q^{22} + 20 q^{23} + 24 q^{24} - 88 q^{25} + 56 q^{26} - 144 q^{28} + 16 q^{30} - 20 q^{31} + 40 q^{32} - 28 q^{34} - 32 q^{35} - 104 q^{36} - 64 q^{37} + 16 q^{38} + 84 q^{40} - 16 q^{41} - 180 q^{42} + 24 q^{43} + 112 q^{44} + 8 q^{45} + 52 q^{46} - 120 q^{47} - 40 q^{49} + 56 q^{50} + 32 q^{51} - 148 q^{52} - 64 q^{53} - 36 q^{54} + 72 q^{55} + 48 q^{56} - 72 q^{57} - 24 q^{59} + 20 q^{60} + 8 q^{61} + 168 q^{62} + 8 q^{63} - 184 q^{64} + 112 q^{65} + 16 q^{66} + 40 q^{67} + 112 q^{68} + 24 q^{69} - 24 q^{70} + 32 q^{71} + 40 q^{73} + 64 q^{74} + 32 q^{75} - 220 q^{76} + 136 q^{77} + 16 q^{78} - 144 q^{79} + 200 q^{80} - 112 q^{81} - 40 q^{82} + 120 q^{83} + 72 q^{84} - 240 q^{85} - 116 q^{86} + 176 q^{88} + 64 q^{89} + 16 q^{90} + 80 q^{91} - 240 q^{92} + 48 q^{93} - 188 q^{94} + 84 q^{95} + 48 q^{96} + 96 q^{97} + 160 q^{98} - 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(667, [\chi])\)\(^{\oplus 2}\)