# Properties

 Label 456.2.u Level $456$ Weight $2$ Character orbit 456.u Rep. character $\chi_{456}(11,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $152$ Newform subspaces $4$ Sturm bound $160$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 456.u (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$456$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$160$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$41$$

## Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

## Trace form

 $$152q - 2q^{3} - 4q^{4} - 5q^{6} - 2q^{9} + O(q^{10})$$ $$152q - 2q^{3} - 4q^{4} - 5q^{6} - 2q^{9} + 8q^{10} + 2q^{12} - 4q^{16} + 6q^{18} - 16q^{19} + 2q^{22} + 3q^{24} - 64q^{25} - 8q^{27} + 6q^{28} + 4q^{30} - 4q^{33} + 8q^{34} + 25q^{36} - 40q^{40} - 18q^{42} - 4q^{43} - 16q^{46} - 19q^{48} - 136q^{49} - 14q^{51} - 26q^{52} - 2q^{54} - 2q^{57} + 64q^{58} - 18q^{60} - 112q^{64} + 9q^{66} - 4q^{67} + 72q^{70} - 29q^{72} + 4q^{73} + 136q^{75} + 32q^{76} - 50q^{78} - 6q^{81} - 54q^{82} + 36q^{84} + 68q^{88} - 22q^{90} + 24q^{91} - 8q^{94} - 98q^{96} + 12q^{97} + 48q^{99} + O(q^{100})$$

## 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.u.a $$4$$ $$3.641$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$$
456.2.u.b $$4$$ $$3.641$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$$
456.2.u.c $$8$$ $$3.641$$ 8.0.4857532416.1 None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{7})q^{2}-\beta _{3}q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots$$
456.2.u.d $$136$$ $$3.641$$ None $$0$$ $$-2$$ $$0$$ $$0$$