# Properties

 Label 3024.1.cg Level $3024$ Weight $1$ Character orbit 3024.cg Rep. character $\chi_{3024}(2161,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $576$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3024.cg (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$576$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3024, [\chi])$$.

Total New Old
Modular forms 108 4 104
Cusp forms 36 4 32
Eisenstein series 72 0 72

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

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

## Trace form

 $$4q + q^{7} + O(q^{10})$$ $$4q + q^{7} - 3q^{19} - 2q^{25} + 6q^{31} + q^{37} - 4q^{43} + q^{49} + q^{67} - 3q^{73} + q^{79} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3024, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3024.1.cg.a $$2$$ $$1.509$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{19}+\zeta_{6}^{2}q^{25}+\cdots$$
3024.1.cg.b $$2$$ $$1.509$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{25}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3024, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3024, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 2}$$