# Properties

 Label 3528.1.bw Level $3528$ Weight $1$ Character orbit 3528.bw Rep. character $\chi_{3528}(325,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $10$ Newform subspaces $3$ Sturm bound $672$ Trace bound $10$

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## Defining parameters

 Level: $$N$$ $$=$$ $$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3528.bw (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: $$10$$

## Dimensions

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

Total New Old
Modular forms 88 18 70
Cusp forms 24 10 14
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

 $$10q - q^{2} + 3q^{4} + 2q^{8} + O(q^{10})$$ $$10q - q^{2} + 3q^{4} + 2q^{8} + 6q^{10} - 5q^{16} - 4q^{22} + 2q^{23} - q^{25} - 6q^{31} - q^{32} + 6q^{40} + 2q^{46} - 2q^{50} - 2q^{58} - 6q^{64} + 4q^{71} + 4q^{79} - 2q^{88} - 4q^{92} + O(q^{100})$$

## 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.bw.a $$2$$ $$1.761$$ $$\Q(\sqrt{-3})$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots$$
3528.1.bw.b $$4$$ $$1.761$$ $$\Q(\zeta_{12})$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{42})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$$
3528.1.bw.c $$4$$ $$1.761$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(3528, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(392, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$