# Properties

 Label 462.2.n Level $462$ Weight $2$ Character orbit 462.n Rep. character $\chi_{462}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $6$ Sturm bound $192$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$231$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$192$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(462, [\chi])$$.

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

## Trace form

 $$64q - 32q^{4} + 8q^{9} + O(q^{10})$$ $$64q - 32q^{4} + 8q^{9} - 16q^{15} - 32q^{16} - 4q^{22} + 44q^{25} - 24q^{27} - 4q^{31} + 26q^{33} - 8q^{34} - 16q^{36} - 4q^{37} - 24q^{42} - 56q^{45} + 4q^{49} + 84q^{55} - 32q^{58} + 8q^{60} + 64q^{64} + 8q^{66} + 8q^{67} - 64q^{69} + 52q^{70} - 52q^{75} - 48q^{78} - 24q^{81} + 16q^{82} + 2q^{88} - 24q^{91} - 44q^{93} + 32q^{97} - 24q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(462, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
462.2.n.a $$4$$ $$3.689$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-2$$ $$-6$$ $$3$$ $$3$$ $$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
462.2.n.b $$4$$ $$3.689$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-2$$ $$6$$ $$-3$$ $$-3$$ $$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$$
462.2.n.c $$4$$ $$3.689$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$2$$ $$-6$$ $$3$$ $$-3$$ $$q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
462.2.n.d $$4$$ $$3.689$$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$2$$ $$6$$ $$-3$$ $$3$$ $$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$$
462.2.n.e $$24$$ $$3.689$$ None $$-12$$ $$0$$ $$0$$ $$0$$
462.2.n.f $$24$$ $$3.689$$ None $$12$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(462, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$