Properties

Label 3549.2.eo
Level $3549$
Weight $2$
Character orbit 3549.eo
Rep. character $\chi_{3549}(136,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $11664$
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.eo (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 23472 11664 11808
Cusp forms 23088 11664 11424
Eisenstein series 384 0 384

Trace form

\( 11664q - 4q^{7} - 486q^{9} + O(q^{10}) \) \( 11664q - 4q^{7} - 486q^{9} + 16q^{11} - 8q^{12} - 32q^{14} + 984q^{16} + 32q^{19} + 12q^{21} - 36q^{24} + 60q^{26} - 32q^{28} + 2q^{31} - 480q^{32} + 8q^{35} + 2q^{37} + 26q^{39} + 60q^{40} - 36q^{41} + 12q^{42} + 36q^{43} - 56q^{44} - 8q^{46} - 44q^{49} + 40q^{50} + 24q^{51} - 44q^{52} - 36q^{55} + 72q^{56} + 38q^{57} - 24q^{58} + 96q^{59} - 28q^{60} + 72q^{62} - 2q^{63} + 88q^{65} - 208q^{67} + 96q^{70} - 36q^{71} + 46q^{73} + 336q^{74} - 28q^{75} - 76q^{76} + 8q^{78} - 204q^{80} + 486q^{81} - 48q^{82} + 48q^{83} - 20q^{84} - 420q^{85} + 288q^{86} - 48q^{89} + 60q^{91} - 72q^{92} - 34q^{93} + 12q^{94} - 72q^{96} + 838q^{97} + 36q^{98} + 8q^{99} + O(q^{100}) \)

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

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