# Properties

 Label 456.2.g Level $456$ Weight $2$ Character orbit 456.g Rep. character $\chi_{456}(229,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $2$ Sturm bound $160$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 456.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$160$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(456, [\chi])$$.

Total New Old
Modular forms 84 36 48
Cusp forms 76 36 40
Eisenstein series 8 0 8

## Trace form

 $$36q + 4q^{2} - 4q^{4} + 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10})$$ $$36q + 4q^{2} - 4q^{4} + 8q^{7} + 4q^{8} - 36q^{9} + 8q^{10} - 8q^{12} - 20q^{14} + 20q^{16} + 8q^{17} - 4q^{18} - 16q^{20} - 20q^{22} - 16q^{23} + 12q^{24} - 44q^{25} + 16q^{26} + 8q^{28} + 8q^{30} + 4q^{32} + 12q^{34} + 4q^{36} + 16q^{39} - 28q^{40} - 8q^{41} - 8q^{42} + 8q^{44} + 52q^{46} - 16q^{48} + 36q^{49} + 8q^{50} - 36q^{52} + 24q^{56} - 16q^{58} + 20q^{60} - 48q^{62} - 8q^{63} - 4q^{64} - 32q^{65} + 8q^{66} + 32q^{68} + 28q^{70} - 48q^{71} - 4q^{72} + 40q^{73} - 56q^{74} - 12q^{78} + 16q^{79} - 8q^{80} + 36q^{81} + 24q^{82} - 8q^{84} - 20q^{86} + 24q^{87} + 40q^{89} - 8q^{90} - 48q^{92} + 8q^{94} - 20q^{96} - 8q^{97} + 8q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(456, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
456.2.g.a $$18$$ $$3.641$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$2$$ $$0$$ $$0$$ $$-12$$ $$q+\beta _{14}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{13}q^{5}+\cdots$$
456.2.g.b $$18$$ $$3.641$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$2$$ $$0$$ $$0$$ $$20$$ $$q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(456, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(456, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 2}$$