# Properties

 Label 462.2.p Level $462$ Weight $2$ Character orbit 462.p Rep. character $\chi_{462}(241,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $2$ Sturm bound $192$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$13$$

## Dimensions

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

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

## Trace form

 $$32q + 16q^{4} + 24q^{5} + 16q^{9} + O(q^{10})$$ $$32q + 16q^{4} + 24q^{5} + 16q^{9} - 8q^{11} + 16q^{14} - 8q^{15} - 16q^{16} + 4q^{22} - 8q^{23} + 20q^{25} + 24q^{26} + 12q^{31} + 6q^{33} + 32q^{36} + 28q^{37} - 24q^{38} + 12q^{42} + 8q^{44} + 24q^{45} - 48q^{47} - 12q^{49} + 8q^{56} - 4q^{60} - 32q^{64} - 32q^{67} - 60q^{70} - 112q^{71} - 24q^{75} - 20q^{77} - 24q^{80} - 16q^{81} - 24q^{82} - 24q^{86} + 2q^{88} - 72q^{89} - 16q^{91} - 16q^{92} + 8q^{93} - 16q^{99} + O(q^{100})$$

## 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.p.a $$16$$ $$3.689$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$-6$$ $$q-\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{13}q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots$$
462.2.p.b $$16$$ $$3.689$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$12$$ $$6$$ $$q-\beta _{12}q^{2}+\beta _{11}q^{3}+(1+\beta _{13})q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$