# Properties

 Label 1176.1.s Level $1176$ Weight $1$ Character orbit 1176.s Rep. character $\chi_{1176}(557,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $3$ Sturm bound $224$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1176 = 2^{3} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1176.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$168$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$224$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1176, [\chi])$$.

Total New Old
Modular forms 52 28 24
Cusp forms 20 12 8
Eisenstein series 32 16 16

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12 q + 2 q^{4} - 4 q^{6} - 2 q^{9} + O(q^{10})$$ $$12 q + 2 q^{4} - 4 q^{6} - 2 q^{9} - 2 q^{10} - 12 q^{15} - 6 q^{16} - 4 q^{18} - 4 q^{22} + 2 q^{24} - 4 q^{25} + 4 q^{30} - 2 q^{31} - 2 q^{33} + 4 q^{36} + 4 q^{39} - 2 q^{40} + 2 q^{54} - 4 q^{55} - 8 q^{57} + 2 q^{58} - 2 q^{60} - 4 q^{64} + 4 q^{72} + 4 q^{73} + 8 q^{78} + 2 q^{79} + 2 q^{81} - 2 q^{87} + 2 q^{88} + 4 q^{90} + 2 q^{96} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1176, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1176.1.s.a $2$ $0.587$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-6})$$ None $$-1$$ $$1$$ $$-1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$$
1176.1.s.b $2$ $0.587$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-6})$$ None $$1$$ $$-1$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
1176.1.s.c $8$ $0.587$ $$\Q(\zeta_{24})$$ $D_{4}$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1176, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1176, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 2}$$