# Properties

 Label 3549.2.cs Level $3549$ Weight $2$ Character orbit 3549.cs Rep. character $\chi_{3549}(100,\cdot)$ Character field $\Q(\zeta_{39})$ Dimension $5832$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.cs (of order $$39$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1183$$ Character field: $$\Q(\zeta_{39})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 11736 5832 5904
Cusp forms 11544 5832 5712
Eisenstein series 192 0 192

## Trace form

 $$5832q - 6q^{3} + 244q^{4} + 3q^{7} - 486q^{9} + O(q^{10})$$ $$5832q - 6q^{3} + 244q^{4} + 3q^{7} - 486q^{9} - 16q^{10} - 8q^{11} + 8q^{12} + 24q^{13} + 12q^{14} + 254q^{16} - 6q^{19} + 8q^{20} + 5q^{21} + 6q^{22} + 24q^{24} + 245q^{25} + 2q^{26} - 6q^{27} - 8q^{28} + 11q^{31} + 110q^{32} + 56q^{34} + 2q^{35} + 244q^{36} - 23q^{37} + 500q^{38} + 8q^{39} + 34q^{40} - 18q^{41} - 128q^{42} - 8q^{43} + 20q^{44} + 8q^{46} - 12q^{47} + 18q^{48} - 155q^{49} + 2q^{50} - 4q^{51} - 48q^{52} + 400q^{53} + 38q^{55} - 10q^{56} + 38q^{57} + 144q^{58} + 240q^{59} - 32q^{60} - 26q^{61} - 24q^{62} + 3q^{63} - 484q^{64} + 48q^{65} + 16q^{66} - 226q^{67} + 110q^{68} + 16q^{69} + 28q^{70} - 166q^{71} - 4q^{73} + 404q^{74} + 29q^{75} + 168q^{76} - 6q^{77} - 10q^{78} + 19q^{79} + 40q^{80} - 486q^{81} - 28q^{82} - 64q^{83} - 22q^{84} - 188q^{85} - 332q^{86} + 30q^{87} - 16q^{89} - 16q^{90} - 117q^{91} + 36q^{92} - 113q^{93} - 58q^{94} - 88q^{95} - 14q^{96} + 133q^{97} + 82q^{98} - 8q^{99} + O(q^{100})$$

## 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

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