Properties

Label 3549.2.dy
Level $3549$
Weight $2$
Character orbit 3549.dy
Rep. character $\chi_{3549}(68,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $11544$
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.dy (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3549 \)
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 11736 0
Cusp forms 11544 11544 0
Eisenstein series 192 192 0

Trace form

\( 11544q - 36q^{3} + 930q^{4} - 12q^{6} - 46q^{7} - 12q^{9} + O(q^{10}) \) \( 11544q - 36q^{3} + 930q^{4} - 12q^{6} - 46q^{7} - 12q^{9} - 72q^{10} - 39q^{12} + 120q^{13} - 95q^{15} - 962q^{16} - 15q^{18} - 57q^{19} - 33q^{21} - 62q^{22} - 21q^{24} + 441q^{25} - 46q^{28} + 89q^{30} - 39q^{31} + 6q^{33} - 48q^{36} - 4q^{37} + 61q^{39} - 168q^{40} - 25q^{42} - 92q^{43} - 39q^{45} + 182q^{46} + 18q^{48} - 52q^{49} - 9q^{51} - 26q^{52} - 273q^{54} + 30q^{55} + 13q^{57} - 4q^{58} - 68q^{60} - 33q^{61} - 119q^{63} + 860q^{64} + 33q^{66} - 59q^{67} + 84q^{69} - 20q^{70} - 30q^{72} - 138q^{73} - 39q^{75} - 324q^{76} + 19q^{78} - 55q^{79} - 12q^{81} - 60q^{82} - 379q^{84} - 102q^{85} - 39q^{87} - 84q^{88} - 50q^{91} + 13q^{93} - 114q^{94} - 69q^{96} + 33q^{97} - 126q^{99} + O(q^{100}) \)

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

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