Properties

Label 2001.2.bk
Level $2001$
Weight $2$
Character orbit 2001.bk
Rep. character $\chi_{2001}(16,\cdot)$
Character field $\Q(\zeta_{77})$
Dimension $7200$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.bk (of order \(77\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{77})\)
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

\( 7200q + 8q^{2} + 128q^{4} + 8q^{7} + 24q^{8} + 120q^{9} + O(q^{10}) \) \( 7200q + 8q^{2} + 128q^{4} + 8q^{7} + 24q^{8} + 120q^{9} - 40q^{11} - 20q^{13} + 8q^{14} + 8q^{15} + 308q^{16} + 8q^{17} + 8q^{18} - 28q^{19} - 92q^{22} - 74q^{23} + 308q^{25} - 32q^{26} - 16q^{28} - 18q^{29} - 16q^{30} + 12q^{31} - 244q^{32} + 16q^{33} + 80q^{34} - 112q^{35} + 84q^{36} + 28q^{37} - 132q^{38} - 72q^{39} + 32q^{40} + 8q^{41} + 24q^{42} - 28q^{43} - 240q^{44} - 120q^{46} - 32q^{47} - 224q^{48} + 88q^{49} - 260q^{50} + 196q^{51} - 228q^{52} + 48q^{53} + 176q^{55} - 232q^{56} - 48q^{57} - 50q^{58} + 48q^{59} + 32q^{60} - 40q^{61} - 180q^{62} + 8q^{63} + 168q^{64} + 16q^{65} - 48q^{66} - 12q^{67} + 72q^{68} - 12q^{69} - 88q^{70} - 44q^{71} - 4q^{72} + 28q^{73} + 210q^{74} + 16q^{75} + 48q^{76} - 120q^{77} + 16q^{78} - 12q^{79} - 220q^{80} + 120q^{81} + 136q^{82} - 88q^{83} + 32q^{84} - 128q^{85} + 1280q^{86} - 80q^{87} - 360q^{88} - 204q^{89} - 308q^{91} + 110q^{92} + 32q^{93} + 80q^{94} - 240q^{95} - 196q^{97} - 532q^{98} + 16q^{99} + O(q^{100}) \)

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

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