# Properties

 Label 3549.2.ei Level $3549$ Weight $2$ Character orbit 3549.ei Rep. character $\chi_{3549}(76,\cdot)$ Character field $\Q(\zeta_{156})$ Dimension $11616$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.ei (of order $$156$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1183$$ 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 11616 11904
Cusp forms 23136 11616 11520
Eisenstein series 384 0 384

## Trace form

 $$11616q + 2q^{7} - 484q^{9} + O(q^{10})$$ $$11616q + 2q^{7} - 484q^{9} + 16q^{11} - 32q^{14} - 472q^{16} + 10q^{21} + 56q^{28} - 480q^{32} + 8q^{35} + 28q^{37} - 8q^{39} + 12q^{42} + 12q^{43} + 16q^{44} + 112q^{46} + 30q^{49} - 176q^{50} + 180q^{56} - 48q^{57} - 48q^{58} + 104q^{60} + 4q^{63} - 32q^{65} + 400q^{67} + 264q^{70} + 24q^{71} + 432q^{74} + 8q^{78} + 484q^{81} - 20q^{84} - 360q^{85} - 576q^{86} - 216q^{88} - 86q^{91} + 144q^{92} - 12q^{93} - 96q^{95} - 36q^{98} - 16q^{99} + O(q^{100})$$

## 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

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