# Properties

 Label 3549.2.em Level $3549$ Weight $2$ Character orbit 3549.em Rep. character $\chi_{3549}(2,\cdot)$ Character field $\Q(\zeta_{156})$ Dimension $23088$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.em (of order $$156$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3549$$ Character field: $$\Q(\zeta_{156})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 23472 23472 0
Cusp forms 23088 23088 0
Eisenstein series 384 384 0

## Trace form

 $$23088q - 28q^{3} - 52q^{4} - 100q^{6} - 96q^{7} - 28q^{9} + O(q^{10})$$ $$23088q - 28q^{3} - 52q^{4} - 100q^{6} - 96q^{7} - 28q^{9} - 40q^{10} - 62q^{12} - 192q^{13} - 98q^{15} + 1820q^{16} - 24q^{18} - 32q^{19} - 46q^{21} - 96q^{22} - 28q^{24} - 52q^{25} - 88q^{27} - 172q^{28} + 164q^{30} - 94q^{31} - 10q^{33} - 160q^{34} - 44q^{36} - 66q^{37} + 172q^{39} - 96q^{40} - 62q^{42} - 100q^{43} - 24q^{45} - 444q^{46} - 80q^{48} - 48q^{49} + 10q^{51} - 92q^{52} - 40q^{54} - 200q^{55} - 114q^{57} - 96q^{58} + 32q^{60} - 56q^{61} - 202q^{63} - 208q^{64} - 90q^{66} - 208q^{67} - 128q^{69} + 208q^{70} - 72q^{72} + 30q^{73} - 286q^{75} - 324q^{76} - 186q^{78} - 20q^{79} - 16q^{81} - 88q^{82} - 224q^{84} - 264q^{85} + 34q^{87} - 392q^{88} - 104q^{90} - 128q^{91} - 72q^{93} + 276q^{94} + 64q^{96} - 270q^{97} - 94q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3549, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.