# Properties

 Label 546.2.bi Level $546$ Weight $2$ Character orbit 546.bi Rep. character $\chi_{546}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $76$ Newform subspaces $6$ Sturm bound $224$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bi (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$224$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(546, [\chi])$$.

Total New Old
Modular forms 240 76 164
Cusp forms 208 76 132
Eisenstein series 32 0 32

## Trace form

 $$76q + 76q^{4} - 2q^{7} - 4q^{9} + O(q^{10})$$ $$76q + 76q^{4} - 2q^{7} - 4q^{9} + 2q^{13} - 12q^{15} + 76q^{16} + 24q^{18} - 14q^{19} + 42q^{25} - 2q^{28} + 2q^{30} - 16q^{31} + 12q^{33} - 4q^{36} + 18q^{39} - 14q^{42} - 10q^{43} - 26q^{49} + 6q^{51} + 2q^{52} - 36q^{54} - 24q^{55} - 12q^{60} - 78q^{61} + 18q^{63} + 76q^{64} + 24q^{66} - 60q^{67} + 54q^{69} + 24q^{72} + 2q^{73} - 14q^{76} + 4q^{78} - 4q^{79} - 4q^{81} - 24q^{82} - 48q^{85} - 80q^{91} - 72q^{94} - 14q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(546, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
546.2.bi.a $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-3$$ $$6$$ $$-1$$ $$q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(4-2\zeta_{6})q^{5}+\cdots$$
546.2.bi.b $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$3$$ $$-4$$ $$q-q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots$$
546.2.bi.c $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-3$$ $$-6$$ $$-1$$ $$q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-4+2\zeta_{6})q^{5}+\cdots$$
546.2.bi.d $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-3$$ $$-3$$ $$-4$$ $$q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots$$
546.2.bi.e $$34$$ $$4.360$$ None $$-34$$ $$3$$ $$-9$$ $$4$$
546.2.bi.f $$34$$ $$4.360$$ None $$34$$ $$6$$ $$9$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(546, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$