# Properties

 Label 3549.2.ej Level $3549$ Weight $2$ Character orbit 3549.ej Rep. character $\chi_{3549}(31,\cdot)$ 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.ej (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

 $$11616q + 2q^{7} - 484q^{9} + O(q^{10})$$ $$11616q + 2q^{7} - 484q^{9} - 8q^{11} + 64q^{14} - 472q^{16} + 30q^{19} - 8q^{21} + 36q^{24} + 60q^{26} - 16q^{28} + 6q^{31} + 240q^{32} - 16q^{35} - 14q^{37} - 2q^{39} - 120q^{40} - 24q^{42} - 8q^{44} + 16q^{46} + 136q^{50} + 144q^{52} + 12q^{57} + 48q^{58} - 96q^{59} + 44q^{60} - 2q^{63} + 16q^{65} - 206q^{67} + 312q^{70} + 72q^{71} + 54q^{73} + 336q^{74} - 64q^{78} + 12q^{80} + 484q^{81} - 20q^{84} + 744q^{85} + 288q^{86} - 72q^{87} - 48q^{89} + 10q^{91} + 144q^{92} - 6q^{93} - 444q^{94} - 132q^{96} - 96q^{98} - 16q^{99} + O(q^{100})$$

## 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

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