# Properties

 Label 476.1.o Level $476$ Weight $1$ Character orbit 476.o Rep. character $\chi_{476}(67,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $3$ Sturm bound $72$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$476 = 2^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 476.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$476$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(476, [\chi])$$.

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8 q - 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 4 q^{21} - 4 q^{25} + 4 q^{26} + 4 q^{33} + 8 q^{36} - 4 q^{42} + 4 q^{53} + 8 q^{64} - 8 q^{66} - 4 q^{68} - 8 q^{69} + 4 q^{72} + 8 q^{77} + 8 q^{84} + 4 q^{93} - 4 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(476, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
476.1.o.a $2$ $0.238$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$-1$$ $$0$$ $$-2$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-q^{7}+\cdots$$
476.1.o.b $2$ $0.238$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$1$$ $$0$$ $$2$$ $$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{7}+\cdots$$
476.1.o.c $4$ $0.238$ $$\Q(\zeta_{12})$$ $D_{6}$ $$\Q(\sqrt{-17})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots$$