Properties

Label 3549.2.dw
Level $3549$
Weight $2$
Character orbit 3549.dw
Rep. character $\chi_{3549}(4,\cdot)$
Character field $\Q(\zeta_{78})$
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.dw (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{78})\)
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

\( 5832q - 3q^{3} + 488q^{4} - 4q^{7} + 243q^{9} + O(q^{10}) \) \( 5832q - 3q^{3} + 488q^{4} - 4q^{7} + 243q^{9} + 8q^{10} + 12q^{11} + 8q^{12} - 24q^{13} + 20q^{14} - 476q^{16} - 3q^{19} + 24q^{20} + 7q^{21} - 6q^{22} - 245q^{25} + 26q^{26} + 6q^{27} - 8q^{28} + 3q^{31} - 260q^{32} + 2q^{35} - 244q^{36} - 280q^{38} - 13q^{39} - 14q^{40} - 18q^{41} + 104q^{42} - 12q^{44} - 36q^{47} - 18q^{48} + 166q^{49} + 102q^{50} - 4q^{51} + 2q^{52} + 224q^{53} - 26q^{55} + 18q^{56} + 64q^{58} - 208q^{59} - 36q^{60} - 13q^{61} + 48q^{62} + 5q^{63} + 468q^{64} + 10q^{65} - 16q^{66} + 33q^{67} + 220q^{68} + 16q^{69} - 348q^{70} + 138q^{71} + 42q^{73} - 184q^{74} - 26q^{75} - 156q^{76} - 42q^{77} + 18q^{78} - 19q^{79} - 48q^{80} + 243q^{81} - 6q^{82} - 28q^{84} - 160q^{85} + 120q^{86} + 36q^{87} - 16q^{90} + 104q^{91} - 108q^{92} - 221q^{93} - 204q^{94} + 104q^{95} + 30q^{96} + 129q^{97} - 102q^{98} + O(q^{100}) \)

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

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