# Properties

 Label 3528.1.bx Level $3528$ Weight $1$ Character orbit 3528.bx Rep. character $\chi_{3528}(667,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $10$ Newform subspaces $3$ Sturm bound $672$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3528.bx (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$672$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3528, [\chi])$$.

Total New Old
Modular forms 92 18 74
Cusp forms 28 10 18
Eisenstein series 64 8 56

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 0 0 0

## Trace form

 $$10q - q^{2} - q^{4} + 2q^{8} + O(q^{10})$$ $$10q - q^{2} - q^{4} + 2q^{8} - 2q^{11} - 5q^{16} - 4q^{22} - 5q^{25} - q^{32} + 4q^{43} - 2q^{44} + 4q^{46} + 2q^{50} - 4q^{58} + 2q^{64} - 2q^{67} - 2q^{86} + 2q^{88} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3528, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3528.1.bx.a $$2$$ $$1.761$$ $$\Q(\sqrt{-3})$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{14})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$$
3528.1.bx.b $$4$$ $$1.761$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$D_{4}$$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+q^{8}+\beta _{2}q^{16}+\cdots$$
3528.1.bx.c $$4$$ $$1.761$$ $$\Q(\zeta_{12})$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-42})$$ $$\Q(\sqrt{6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3528, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3528, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(392, [\chi])$$$$^{\oplus 3}$$