# Properties

 Label 3549.2.eb Level $3549$ Weight $2$ Character orbit 3549.eb Rep. character $\chi_{3549}(115,\cdot)$ Character field $\Q(\zeta_{156})$ Dimension $11664$ Sturm bound $970$

# Related objects

## Defining parameters

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

 $$11664q + 4q^{7} + 972q^{9} + O(q^{10})$$ $$11664q + 4q^{7} + 972q^{9} - 8q^{11} + 8q^{12} - 32q^{14} - 492q^{16} + 10q^{19} - 2q^{21} + 60q^{26} - 4q^{28} - 8q^{31} + 240q^{32} - 16q^{35} - 16q^{37} - 16q^{39} + 60q^{40} + 36q^{41} - 24q^{42} + 36q^{43} + 64q^{44} + 52q^{46} + 14q^{49} + 40q^{50} - 24q^{51} - 100q^{52} + 36q^{55} - 36q^{56} + 38q^{57} + 72q^{58} + 44q^{60} - 72q^{62} - 4q^{63} - 56q^{65} + 398q^{67} - 264q^{70} - 36q^{71} + 38q^{73} - 792q^{74} - 14q^{75} + 76q^{76} + 8q^{78} - 96q^{80} - 972q^{81} - 96q^{82} - 48q^{83} - 72q^{84} - 420q^{85} - 576q^{86} - 36q^{87} - 48q^{89} - 26q^{91} - 72q^{92} + 14q^{93} + 468q^{94} - 48q^{95} - 12q^{96} - 838q^{97} + 72q^{98} + 8q^{99} + O(q^{100})$$

## 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

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