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

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

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

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