# Properties

 Label 3549.2.j Level $3549$ Weight $2$ Character orbit 3549.j Rep. character $\chi_{3549}(991,\cdot)$ Character field $\Q(\zeta_{3})$ 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.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{3})$$ 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

 $$410q - 6q^{3} - 204q^{4} + 3q^{7} + 410q^{9} + O(q^{10})$$ $$410q - 6q^{3} - 204q^{4} + 3q^{7} + 410q^{9} - 16q^{10} - 8q^{11} + 8q^{12} + 20q^{14} - 194q^{16} - 8q^{17} - 6q^{19} + 8q^{20} + 5q^{21} - 2q^{22} + 8q^{23} + 24q^{24} - 195q^{25} - 6q^{27} - 8q^{28} + 11q^{31} - 20q^{32} + 56q^{34} + 2q^{35} - 204q^{36} - 23q^{37} - 28q^{38} + 34q^{40} - 18q^{41} + 2q^{42} + 20q^{44} + 8q^{46} - 12q^{47} + 18q^{48} - 7q^{49} + 2q^{50} - 12q^{51} - 32q^{53} + 30q^{55} - 58q^{56} + 38q^{57} + 40q^{58} + 32q^{59} - 32q^{60} - 10q^{61} - 8q^{62} + 3q^{63} + 412q^{64} + 16q^{66} + 34q^{67} - 44q^{68} + 8q^{69} - 76q^{70} - 10q^{71} - 4q^{73} - 12q^{74} + 29q^{75} + 12q^{76} + 26q^{77} + 19q^{79} + 40q^{80} + 410q^{81} - 28q^{82} - 64q^{83} - 22q^{84} + 20q^{85} - 20q^{86} + 30q^{87} + 48q^{88} - 16q^{89} - 16q^{90} - 28q^{92} + 17q^{93} - 120q^{94} + 56q^{95} - 14q^{96} - 23q^{97} + 82q^{98} - 8q^{99} + O(q^{100})$$

## 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

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