# Properties

 Label 546.2.p Level $546$ Weight $2$ Character orbit 546.p Rep. character $\chi_{546}(239,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $4$ 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.p (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ 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 56 184
Cusp forms 208 56 152
Eisenstein series 32 0 32

## Trace form

 $$56q + O(q^{10})$$ $$56q - 56q^{16} + 8q^{18} - 16q^{19} - 8q^{21} + 48q^{27} + 16q^{31} - 48q^{33} + 16q^{37} - 16q^{39} - 32q^{45} - 8q^{46} + 48q^{54} + 32q^{55} + 80q^{57} - 8q^{58} + 32q^{61} - 8q^{63} + 32q^{66} - 24q^{67} + 8q^{72} - 16q^{73} - 16q^{76} + 80q^{78} - 80q^{79} - 48q^{81} + 8q^{84} + 80q^{85} - 8q^{91} - 48q^{93} + 16q^{94} + 128q^{97} - 88q^{99} + O(q^{100})$$

## 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.p.a $$8$$ $$4.360$$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$$
546.2.p.b $$8$$ $$4.360$$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$$
546.2.p.c $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{8}q^{2}+\beta _{11}q^{3}-\beta _{4}q^{4}+(\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots$$
546.2.p.d $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{8}q^{2}-\beta _{19}q^{3}-\beta _{4}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$