# Properties

 Label 3549.2.cy Level $3549$ Weight $2$ Character orbit 3549.cy Rep. character $\chi_{3549}(17,\cdot)$ 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.cy (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

 $$11544q - 36q^{3} - 974q^{4} - 50q^{7} - 16q^{9} + O(q^{10})$$ $$11544q - 36q^{3} - 974q^{4} - 50q^{7} - 16q^{9} - 72q^{10} - 27q^{12} - 120q^{13} + 9q^{15} - 946q^{16} + 23q^{18} - 79q^{19} - 17q^{21} - 34q^{22} - 27q^{24} - 485q^{25} - 62q^{28} + 107q^{30} - 107q^{31} - 24q^{33} + 24q^{34} - 52q^{36} - 26q^{37} + 103q^{39} - 24q^{40} - 61q^{42} - 100q^{43} - 33q^{45} + 182q^{46} + 42q^{48} - 52q^{49} + 7q^{51} - 26q^{52} + 177q^{54} - 30q^{55} - 91q^{57} - 108q^{58} - 4q^{60} - 111q^{61} - 91q^{63} - 956q^{64} + 117q^{66} + 155q^{67} + 156q^{69} - 228q^{70} + 110q^{72} - 56q^{73} - 39q^{75} + 296q^{76} - 41q^{78} - 13q^{79} + 4q^{81} - 12q^{82} + 447q^{84} - 74q^{85} - 39q^{87} - 100q^{88} - 174q^{91} - 13q^{93} - 162q^{94} - 15q^{96} - 7q^{97} + O(q^{100})$$

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

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