# Properties

 Label 3549.2.bt Level $3549$ Weight $2$ Character orbit 3549.bt Rep. character $\chi_{3549}(418,\cdot)$ 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.bt (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

 $$820q - 4q^{7} + 410q^{9} + O(q^{10})$$ $$820q - 4q^{7} + 410q^{9} + 16q^{11} - 8q^{12} - 16q^{14} - 808q^{16} + 32q^{19} + 12q^{21} - 16q^{22} - 36q^{24} - 32q^{28} - 32q^{29} + 2q^{31} + 40q^{32} + 8q^{35} + 2q^{37} + 60q^{40} - 36q^{41} + 12q^{42} + 36q^{43} - 56q^{44} - 8q^{46} - 44q^{49} + 40q^{50} + 24q^{51} + 32q^{53} + 12q^{55} + 72q^{56} + 38q^{57} - 24q^{58} + 96q^{59} - 28q^{60} + 144q^{61} + 72q^{62} - 2q^{63} - 112q^{70} - 36q^{71} + 46q^{73} - 80q^{74} - 28q^{75} - 76q^{76} - 204q^{80} - 410q^{81} - 48q^{82} + 48q^{83} - 20q^{84} - 4q^{85} - 24q^{86} - 48q^{89} - 200q^{92} - 34q^{93} + 60q^{94} - 72q^{96} - 98q^{97} + 36q^{98} + 8q^{99} + O(q^{100})$$

## 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

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