Properties

 Label 285.2.b Level $285$ Weight $2$ Character orbit 285.b Rep. character $\chi_{285}(284,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $3$ Sturm bound $80$ Trace bound $4$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 285.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$285$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$80$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

Dimensions

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

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

 $$36q - 44q^{4} + 4q^{6} - 4q^{9} + O(q^{10})$$ $$36q - 44q^{4} + 4q^{6} - 4q^{9} + 36q^{16} - 16q^{19} + 20q^{24} - 16q^{25} - 12q^{30} - 4q^{36} - 8q^{39} - 36q^{45} + 4q^{49} + 12q^{54} + 28q^{55} - 44q^{64} + 72q^{76} + 36q^{81} - 84q^{85} - 76q^{96} + 88q^{99} + O(q^{100})$$

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.b.a $$4$$ $$2.276$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots$$
285.2.b.b $$16$$ $$2.276$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ $$\Q(\sqrt{-95})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots$$
285.2.b.c $$16$$ $$2.276$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$$