# Properties

 Label 3549.2.el Level $3549$ Weight $2$ Character orbit 3549.el Rep. character $\chi_{3549}(11,\cdot)$ 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.el (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

 $$23088q - 22q^{3} - 40q^{4} - 100q^{6} - 88q^{7} - 22q^{9} + O(q^{10})$$ $$23088q - 22q^{3} - 40q^{4} - 100q^{6} - 88q^{7} - 22q^{9} - 52q^{10} + 10q^{12} - 192q^{13} - 98q^{15} - 988q^{16} - 48q^{18} - 38q^{19} - 28q^{21} - 96q^{22} - 22q^{24} - 52q^{25} - 88q^{27} - 32q^{28} - 130q^{30} - 40q^{31} - 76q^{33} - 160q^{34} - 44q^{36} - 60q^{37} - 146q^{39} - 96q^{40} - 44q^{42} - 100q^{43} - 84q^{45} + 108q^{46} - 80q^{48} - 106q^{49} - 62q^{51} - 32q^{52} - 4q^{54} - 200q^{55} - 114q^{57} - 24q^{58} - 22q^{60} - 44q^{61} + 188q^{63} - 208q^{64} + 144q^{66} + 290q^{67} - 128q^{69} - 584q^{70} + 72q^{72} - 114q^{73} + 146q^{75} - 324q^{76} - 186q^{78} - 20q^{79} - 46q^{81} - 52q^{82} - 56q^{84} - 264q^{85} - 56q^{87} + 364q^{88} - 104q^{90} - 82q^{91} - 42q^{93} - 240q^{94} + 28q^{96} - 270q^{97} - 94q^{99} + O(q^{100})$$

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

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