# Properties

 Label 546.2.bn Level $546$ Weight $2$ Character orbit 546.bn Rep. character $\chi_{546}(101,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $76$ Newform subspaces $6$ Sturm bound $224$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bn (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: $$3$$ 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

 $$76q - 38q^{4} + 2q^{7} + 8q^{9} + O(q^{10})$$ $$76q - 38q^{4} + 2q^{7} + 8q^{9} - 2q^{13} - 12q^{15} - 38q^{16} - 24q^{18} - 28q^{19} + 42q^{25} - 4q^{28} - 4q^{30} + 16q^{31} + 24q^{33} - 4q^{36} + 42q^{37} + 12q^{39} + 16q^{42} - 10q^{43} - 12q^{46} - 14q^{49} + 6q^{51} - 14q^{52} - 18q^{54} + 24q^{55} + 12q^{60} + 12q^{63} + 76q^{64} + 24q^{66} - 54q^{69} - 2q^{73} - 108q^{75} + 14q^{76} + 4q^{78} - 4q^{79} + 8q^{81} - 48q^{85} - 24q^{87} - 32q^{91} - 12q^{93} + 14q^{97} + O(q^{100})$$

## 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.bn.a $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$-3$$ $$1$$ $$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.bn.b $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-6$$ $$-5$$ $$q-\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.bn.c $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$6$$ $$-5$$ $$q+\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.bn.d $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$3$$ $$1$$ $$q+\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.bn.e $$34$$ $$4.360$$ None $$-17$$ $$3$$ $$9$$ $$5$$
546.2.bn.f $$34$$ $$4.360$$ None $$17$$ $$-3$$ $$-9$$ $$5$$

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

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