# Properties

 Label 287.1.d Level $287$ Weight $1$ Character orbit 287.d Rep. character $\chi_{287}(286,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $28$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$287 = 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 287.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$287$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$28$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(287, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + O(q^{10})$$ $$6q - 2q^{2} + 4q^{4} - 4q^{8} + 4q^{9} + 2q^{16} - 6q^{18} - 2q^{21} - 2q^{23} + 6q^{25} - 6q^{32} - 2q^{36} - 2q^{37} - 4q^{39} - 4q^{42} - 2q^{43} - 4q^{46} + 6q^{49} - 2q^{50} - 4q^{51} - 4q^{57} + 2q^{72} + 10q^{74} + 6q^{78} + 2q^{81} + 8q^{84} - 4q^{86} - 2q^{91} + 8q^{92} - 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(287, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
287.1.d.a $$3$$ $$0.143$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-287})$$ None $$-1$$ $$-1$$ $$0$$ $$3$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$
287.1.d.b $$3$$ $$0.143$$ $$\Q(\zeta_{14})^+$$ $$D_{7}$$ $$\Q(\sqrt{-287})$$ None $$-1$$ $$1$$ $$0$$ $$-3$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$