Properties

Label 3549.2.cq
Level $3549$
Weight $2$
Character orbit 3549.cq
Rep. character $\chi_{3549}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $5832$
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.cq (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 11736 5832 5904
Cusp forms 11544 5832 5712
Eisenstein series 192 0 192

Trace form

\( 5832q + 3q^{3} - 488q^{4} + 243q^{9} + O(q^{10}) \) \( 5832q + 3q^{3} - 488q^{4} + 243q^{9} + 8q^{10} + 4q^{11} + 8q^{12} + 24q^{13} + 12q^{14} - 508q^{16} + 3q^{19} + 8q^{20} + 5q^{21} + 6q^{22} - 12q^{24} + 245q^{25} - 46q^{26} - 6q^{27} + 16q^{28} + 11q^{31} - 220q^{32} + 56q^{34} - 10q^{35} + 244q^{36} + 46q^{37} - 280q^{38} - 13q^{39} + 34q^{40} - 18q^{41} - 116q^{42} - 8q^{43} + 20q^{44} - 16q^{46} - 12q^{47} + 18q^{48} - 170q^{49} + 2q^{50} - 4q^{51} + 66q^{52} - 224q^{53} + 38q^{55} + 62q^{56} + 38q^{57} - 72q^{58} + 144q^{59} - 32q^{60} + 13q^{61} - 24q^{62} - 3q^{63} - 484q^{64} + 30q^{65} + 16q^{66} + 191q^{67} - 220q^{68} + 16q^{69} + 28q^{70} - 166q^{71} - 4q^{73} - 184q^{74} - 58q^{75} + 168q^{76} - 6q^{77} - 10q^{78} + 19q^{79} - 20q^{80} + 243q^{81} + 14q^{82} - 64q^{83} + 8q^{84} - 188q^{85} + 136q^{86} - 60q^{87} + 32q^{89} - 16q^{90} - 108q^{91} + 36q^{92} + 187q^{93} - 88q^{94} - 136q^{95} - 14q^{96} + 133q^{97} + 58q^{98} - 8q^{99} + O(q^{100}) \)

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

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