# Properties

 Label 285.2.bf Level $285$ Weight $2$ Character orbit 285.bf Rep. character $\chi_{285}(14,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $216$ Newform subspaces $3$ Sturm bound $80$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 285.bf (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$285$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$3$$ Sturm bound: $$80$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(285, [\chi])$$.

Total New Old
Modular forms 264 264 0
Cusp forms 216 216 0
Eisenstein series 48 48 0

## Trace form

 $$216q - 18q^{4} - 12q^{6} - 12q^{9} + O(q^{10})$$ $$216q - 18q^{4} - 12q^{6} - 12q^{9} - 12q^{10} + 15q^{15} - 18q^{16} - 48q^{19} - 30q^{21} - 84q^{24} - 12q^{25} - 24q^{30} - 36q^{31} + 18q^{34} + 12q^{36} - 66q^{40} - 30q^{45} + 36q^{46} - 24q^{49} + 96q^{51} - 60q^{54} - 90q^{55} - 90q^{60} + 12q^{61} - 30q^{64} + 108q^{66} - 18q^{69} - 18q^{70} - 84q^{76} - 120q^{79} + 36q^{81} + 198q^{84} + 54q^{85} + 66q^{90} - 72q^{91} - 72q^{96} + 78q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(285, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
285.2.bf.a $$12$$ $$2.276$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-15})$$ $$-9$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots$$
285.2.bf.b $$12$$ $$2.276$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-15})$$ $$9$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots$$
285.2.bf.c $$192$$ $$2.276$$ None $$0$$ $$0$$ $$0$$ $$0$$