# Properties

 Label 462.2.bf Level $462$ Weight $2$ Character orbit 462.bf Rep. character $\chi_{462}(5,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $256$ Newform subspaces $1$ Sturm bound $192$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.bf (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$231$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 832 256 576
Cusp forms 704 256 448
Eisenstein series 128 0 128

## Trace form

 $$256q - 32q^{4} + 4q^{7} - 12q^{9} + O(q^{10})$$ $$256q - 32q^{4} + 4q^{7} - 12q^{9} + 12q^{10} + 24q^{15} + 32q^{16} - 8q^{18} - 16q^{21} - 12q^{22} + 48q^{25} + 6q^{28} + 18q^{31} - 132q^{33} + 16q^{36} + 4q^{37} - 18q^{40} - 4q^{42} + 64q^{43} - 48q^{45} + 8q^{46} + 76q^{49} - 8q^{51} - 88q^{57} + 46q^{58} - 8q^{60} - 12q^{63} + 64q^{64} - 120q^{66} - 32q^{67} - 58q^{70} - 12q^{72} - 96q^{73} - 204q^{75} - 32q^{78} - 4q^{79} - 64q^{81} + 24q^{82} - 36q^{84} + 232q^{85} - 228q^{87} - 6q^{88} + 40q^{91} - 2q^{93} - 144q^{94} + 160q^{99} + O(q^{100})$$

## 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.bf.a $$256$$ $$3.689$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

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