# Properties

 Label 3549.2.bd Level $3549$ Weight $2$ Character orbit 3549.bd Rep. character $\chi_{3549}(316,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $304$ Sturm bound $970$

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## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.bd (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$970$$

## Dimensions

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

Total New Old
Modular forms 1028 304 724
Cusp forms 916 304 612
Eisenstein series 112 0 112

## Trace form

 $$304q + 148q^{4} - 152q^{9} + O(q^{10})$$ $$304q + 148q^{4} - 152q^{9} + 16q^{10} + 12q^{11} - 32q^{12} + 12q^{15} - 156q^{16} - 8q^{17} - 24q^{20} + 12q^{22} + 12q^{23} - 336q^{25} - 4q^{29} + 8q^{30} - 12q^{33} - 8q^{35} + 148q^{36} - 12q^{37} + 56q^{38} + 136q^{40} + 12q^{41} + 4q^{42} + 16q^{43} + 12q^{45} + 12q^{46} - 16q^{48} + 152q^{49} - 60q^{50} + 24q^{51} - 32q^{53} - 28q^{55} - 12q^{58} + 84q^{59} + 4q^{61} + 28q^{62} - 384q^{64} + 48q^{66} - 12q^{67} - 40q^{68} - 4q^{69} - 48q^{74} + 32q^{75} - 48q^{76} - 16q^{77} - 64q^{79} - 144q^{80} - 152q^{81} + 100q^{82} - 24q^{85} - 32q^{87} - 36q^{88} - 96q^{89} - 32q^{90} + 216q^{92} - 8q^{94} + 48q^{95} + 60q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(3549, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1183, [\chi])$$$$^{\oplus 2}$$