# Properties

 Label 456.2.bu Level $456$ Weight $2$ Character orbit 456.bu Rep. character $\chi_{456}(35,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $456$ Newform subspaces $3$ 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.bu (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$456$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$3$$ Sturm bound: $$160$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 504 504 0
Cusp forms 456 456 0
Eisenstein series 48 48 0

## Trace form

 $$456q - 12q^{3} - 6q^{4} - 6q^{6} - 12q^{9} + O(q^{10})$$ $$456q - 12q^{3} - 6q^{4} - 6q^{6} - 12q^{9} - 18q^{10} - 3q^{12} - 6q^{16} - 12q^{18} - 24q^{19} - 24q^{22} + 6q^{24} - 24q^{25} - 6q^{27} - 36q^{28} - 48q^{30} - 30q^{33} - 54q^{34} + 54q^{36} + 18q^{40} - 51q^{42} - 24q^{43} - 6q^{46} + 69q^{48} + 144q^{49} - 12q^{51} + 12q^{52} + 21q^{54} - 12q^{57} - 96q^{58} + 48q^{60} - 48q^{64} - 54q^{66} - 24q^{67} - 162q^{70} + 12q^{72} - 48q^{73} - 192q^{75} - 132q^{76} + 3q^{78} - 156q^{82} - 45q^{84} - 126q^{88} + 24q^{90} - 108q^{91} - 48q^{94} + 138q^{96} - 24q^{97} - 66q^{99} + O(q^{100})$$

## 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.bu.a $$12$$ $$3.641$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(-\beta _{1}+\beta _{10})q^{3}-2\beta _{4}q^{4}+\cdots$$
456.2.bu.b $$12$$ $$3.641$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-2})$$ $$0$$ $$6$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{9})q^{3}-2\beta _{4}q^{4}+\cdots$$
456.2.bu.c $$432$$ $$3.641$$ None $$0$$ $$-18$$ $$0$$ $$0$$