# Properties

 Label 3549.2.bl Level $3549$ Weight $2$ Character orbit 3549.bl Rep. character $\chi_{3549}(361,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $410$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.bl (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 1026 410 616
Cusp forms 914 410 504
Eisenstein series 112 0 112

## Trace form

 $$410q + 6q^{3} + 204q^{4} + q^{7} + 410q^{9} + O(q^{10})$$ $$410q + 6q^{3} + 204q^{4} + q^{7} + 410q^{9} - 16q^{10} + 8q^{12} + 28q^{14} - 210q^{16} + 8q^{17} + 24q^{20} - 7q^{21} - 14q^{22} - 8q^{23} + 195q^{25} + 6q^{27} + 44q^{28} - 3q^{31} + 14q^{35} + 204q^{36} + 15q^{37} - 12q^{38} - 14q^{40} - 18q^{41} + 22q^{42} - 8q^{43} + 12q^{44} - 12q^{46} + 36q^{47} - 18q^{48} + 33q^{49} + 102q^{50} + 4q^{51} - 34q^{55} + 30q^{56} + 48q^{59} + 36q^{60} + 42q^{61} + 32q^{62} + q^{63} - 428q^{64} - 16q^{66} - 4q^{68} + 24q^{69} + 36q^{70} - 18q^{71} - 42q^{73} - 12q^{74} + 13q^{75} - 74q^{77} - 19q^{79} + 410q^{81} + 12q^{82} - 50q^{84} + 48q^{85} + 36q^{86} - 18q^{87} - 48q^{88} + 48q^{89} - 16q^{90} - 172q^{92} - 3q^{93} + 112q^{94} - 40q^{95} - 30q^{96} - 27q^{97} + 30q^{98} + O(q^{100})$$

## 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

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