Properties

Label 3549.2.ct
Level $3549$
Weight $2$
Character orbit 3549.ct
Rep. character $\chi_{3549}(79,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $5808$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.ct (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 11760 5808 5952
Cusp forms 11568 5808 5760
Eisenstein series 192 0 192

Trace form

\( 5808q + 2q^{3} + 240q^{4} + 2q^{7} + 242q^{9} + O(q^{10}) \) \( 5808q + 2q^{3} + 240q^{4} + 2q^{7} + 242q^{9} + 8q^{10} - 8q^{11} + 4q^{12} - 72q^{13} - 24q^{14} + 220q^{16} - 14q^{19} + 32q^{20} - 8q^{21} + 24q^{22} - 12q^{24} + 238q^{25} + 2q^{26} - 4q^{27} + 24q^{28} + 6q^{31} + 110q^{32} - 16q^{34} - 16q^{35} - 480q^{36} - 10q^{37} - 220q^{38} + q^{39} + 4q^{40} + 72q^{41} - 98q^{42} - 28q^{43} - 40q^{44} - 40q^{46} + 24q^{47} - 16q^{48} + 282q^{49} + 8q^{50} + 8q^{51} - 10q^{52} - 176q^{53} - 40q^{55} + 8q^{56} + 12q^{57} + 12q^{58} + 192q^{59} + 4q^{60} + 32q^{61} - 96q^{62} + 2q^{63} - 416q^{64} - 6q^{65} + 16q^{66} + 66q^{67} + 110q^{68} - 32q^{69} - 200q^{70} - 100q^{71} - 42q^{73} - 184q^{74} - 2q^{75} - 224q^{76} - 60q^{77} - 4q^{78} - 10q^{79} - 68q^{80} + 242q^{81} - 40q^{82} - 16q^{83} - 20q^{84} + 376q^{85} + 100q^{86} + 12q^{87} + 32q^{89} - 16q^{90} + 221q^{91} + 144q^{92} + 33q^{93} + 38q^{94} - 136q^{95} - 44q^{96} - 352q^{97} - 56q^{98} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)