# Properties

 Label 3549.2.cg Level $3549$ Weight $2$ Character orbit 3549.cg Rep. character $\chi_{3549}(19,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $820$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.cg (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 2052 820 1232
Cusp forms 1828 820 1008
Eisenstein series 224 0 224

## Trace form

 $$820q + 4q^{7} - 820q^{9} + O(q^{10})$$ $$820q + 4q^{7} - 820q^{9} - 8q^{11} + 8q^{12} - 16q^{14} + 404q^{16} + 10q^{19} - 2q^{21} - 16q^{22} - 4q^{28} - 32q^{29} - 8q^{31} - 20q^{32} - 16q^{35} - 16q^{37} + 60q^{40} + 36q^{41} - 24q^{42} + 36q^{43} + 64q^{44} + 52q^{46} + 14q^{49} + 40q^{50} - 24q^{51} + 32q^{53} - 12q^{55} - 36q^{56} + 38q^{57} + 72q^{58} + 44q^{60} - 72q^{62} - 4q^{63} - 18q^{67} + 144q^{68} + 152q^{70} - 36q^{71} + 38q^{73} + 40q^{74} - 14q^{75} + 76q^{76} - 96q^{80} + 820q^{81} - 96q^{82} - 48q^{83} - 72q^{84} - 4q^{85} + 48q^{86} - 36q^{87} - 48q^{89} - 200q^{92} + 14q^{93} - 48q^{95} - 12q^{96} + 98q^{97} + 72q^{98} + 8q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3549, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1183, [\chi])$$$$^{\oplus 2}$$