# Properties

 Label 3549.2.ee Level $3549$ Weight $2$ Character orbit 3549.ee Rep. character $\chi_{3549}(50,\cdot)$ Character field $\Q(\zeta_{156})$ Dimension $17472$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.ee (of order $$156$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$507$$ 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 23520 17472 6048
Cusp forms 23136 17472 5664
Eisenstein series 384 0 384

## Trace form

 $$17472q + 12q^{6} + O(q^{10})$$ $$17472q + 12q^{6} + 48q^{10} + 32q^{13} - 4q^{15} - 728q^{16} + 16q^{18} + 8q^{19} + 4q^{21} - 224q^{24} - 24q^{27} + 176q^{30} - 16q^{31} - 48q^{34} - 12q^{36} - 48q^{37} + 48q^{39} - 232q^{45} - 72q^{46} - 24q^{48} + 144q^{52} + 108q^{54} + 448q^{55} + 28q^{57} + 120q^{58} + 116q^{60} + 48q^{61} - 16q^{63} - 104q^{66} + 16q^{67} - 72q^{69} - 48q^{70} - 52q^{72} + 16q^{73} - 60q^{75} - 16q^{76} + 4q^{78} + 16q^{79} - 12q^{81} + 400q^{82} - 72q^{84} + 40q^{85} + 24q^{87} - 72q^{88} - 16q^{91} - 352q^{93} + 648q^{96} - 96q^{97} + 144q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3549, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 2}$$