# Properties

 Label 3549.2.bw Level $3549$ Weight $2$ Character orbit 3549.bw Rep. character $\chi_{3549}(695,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $1564$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.bw (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 2052 1724 328
Cusp forms 1828 1564 264
Eisenstein series 224 160 64

## Trace form

 $$1564q + 4q^{3} + 12q^{4} + 4q^{6} + 16q^{7} + 4q^{9} + O(q^{10})$$ $$1564q + 4q^{3} + 12q^{4} + 4q^{6} + 16q^{7} + 4q^{9} + 36q^{12} + 6q^{15} + 664q^{16} - 22q^{18} + 14q^{19} + 24q^{21} + 8q^{22} + 4q^{24} - 32q^{27} + 72q^{28} + 12q^{31} - 50q^{33} + 48q^{34} + 60q^{36} - 8q^{37} - 92q^{40} - 96q^{42} + 108q^{43} - 58q^{45} - 48q^{46} + 32q^{48} - 2q^{49} - 36q^{51} + 22q^{54} + 24q^{55} - 10q^{57} + 28q^{58} + 4q^{60} + 72q^{61} - 20q^{63} + 30q^{66} - 74q^{67} + 54q^{69} - 64q^{70} + 98q^{72} - 62q^{73} + 42q^{75} - 116q^{76} - 32q^{79} + 44q^{81} - 4q^{84} - 56q^{85} + 106q^{87} - 16q^{93} - 32q^{94} + 54q^{96} - 62q^{97} + 10q^{99} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3549, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$