# Properties

 Label 1476.1.o Level $1476$ Weight $1$ Character orbit 1476.o Rep. character $\chi_{1476}(655,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $4$ Sturm bound $252$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1476 = 2^{2} \cdot 3^{2} \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1476.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1476$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$252$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1476, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 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 16 0 0 0

## Trace form

 $$16 q - 8 q^{4} + O(q^{10})$$ $$16 q - 8 q^{4} - 8 q^{16} - 8 q^{25} - 8 q^{41} + 16 q^{42} - 8 q^{45} - 8 q^{49} + 8 q^{50} - 8 q^{57} + 16 q^{64} - 8 q^{66} + 8 q^{77} - 8 q^{90} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1476, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1476.1.o.a $2$ $0.737$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-41})$$ None $$-1$$ $$-2$$ $$1$$ $$-1$$ $$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$$
1476.1.o.b $2$ $0.737$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-41})$$ None $$-1$$ $$2$$ $$1$$ $$1$$ $$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$$
1476.1.o.c $4$ $0.737$ $$\Q(\zeta_{12})$$ $D_{6}$ $$\Q(\sqrt{-41})$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$$
1476.1.o.d $8$ $0.737$ $$\Q(\zeta_{24})$$ $D_{12}$ $$\Q(\sqrt{-41})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots$$