Properties

 Label 3528.1.cu Level $3528$ Weight $1$ Character orbit 3528.cu Rep. character $\chi_{3528}(1745,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $672$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3528.cu (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$672$$ Trace bound: $$0$$

Dimensions

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

Total New Old
Modular forms 180 4 176
Cusp forms 52 4 48
Eisenstein series 128 0 128

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 0 0 4 0

Trace form

 $$4q + O(q^{10})$$ $$4q + 4q^{13} - 2q^{19} + 2q^{25} - 2q^{31} - 2q^{37} - 4q^{43} + 8q^{55} + 2q^{67} + 2q^{73} - 2q^{79} + O(q^{100})$$

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.cu.a $$4$$ $$1.761$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}+q^{13}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(3528, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 4}$$