# Properties

 Label 462.2.c Level $462$ Weight $2$ Character orbit 462.c Rep. character $\chi_{462}(197,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $2$ Sturm bound $192$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

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

Total New Old
Modular forms 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

## Trace form

 $$24q + 8q^{3} + 24q^{4} + O(q^{10})$$ $$24q + 8q^{3} + 24q^{4} + 8q^{12} + 8q^{15} + 24q^{16} + 16q^{22} - 56q^{25} - 16q^{27} + 24q^{31} + 8q^{34} - 24q^{45} + 8q^{48} - 24q^{49} + 8q^{55} - 16q^{58} + 8q^{60} + 24q^{64} - 32q^{66} + 48q^{67} - 40q^{69} + 8q^{70} - 80q^{75} + 72q^{78} + 8q^{81} - 40q^{82} + 16q^{88} - 48q^{91} - 48q^{93} - 96q^{97} + 56q^{99} + O(q^{100})$$

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

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

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$