# Properties

 Label 3549.2.dk Level $3549$ Weight $2$ Character orbit 3549.dk Rep. character $\chi_{3549}(152,\cdot)$ Character field $\Q(\zeta_{78})$ Dimension $11544$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.dk (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

 $$11544q - 39q^{3} - 504q^{4} + 12q^{6} - 43q^{7} - 15q^{9} + O(q^{10})$$ $$11544q - 39q^{3} - 504q^{4} + 12q^{6} - 43q^{7} - 15q^{9} - 78q^{10} - 39q^{12} - 120q^{13} - 95q^{15} + 442q^{16} - 15q^{18} - 33q^{21} - 62q^{22} - 39q^{24} + 441q^{25} - 4q^{28} - 61q^{30} - 39q^{31} - 39q^{33} - 48q^{36} - 37q^{37} - 44q^{39} - 168q^{40} - 4q^{42} - 92q^{43} - 36q^{45} - 130q^{46} - 18q^{48} - 67q^{49} - 9q^{51} - 118q^{52} - 246q^{54} - 30q^{55} + 13q^{57} - 70q^{58} - 68q^{60} - 78q^{61} + 163q^{63} + 860q^{64} - 84q^{66} - 116q^{67} - 84q^{69} - 20q^{70} + 21q^{72} - 138q^{73} + 114q^{75} + 324q^{76} + 19q^{78} - 55q^{79} - 15q^{81} - 78q^{82} + 209q^{84} - 102q^{85} - 42q^{87} + 90q^{88} + 23q^{91} - 26q^{93} - 312q^{94} - 69q^{96} - 33q^{97} - 126q^{99} + O(q^{100})$$

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

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