# Properties

 Label 3332.1.be Level $3332$ Weight $1$ Character orbit 3332.be Rep. character $\chi_{3332}(407,\cdot)$ Character field $\Q(\zeta_{14})$ Dimension $24$ Newform subspaces $3$ Sturm bound $504$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.be (of order $$14$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3332$$ Character field: $$\Q(\zeta_{14})$$ Newform subspaces: $$3$$ Sturm bound: $$504$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3332, [\chi])$$.

Total New Old
Modular forms 48 48 0
Cusp forms 24 24 0
Eisenstein series 24 24 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24 q - 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$24 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 4 q^{21} - 4 q^{25} - 8 q^{26} - 8 q^{33} - 4 q^{36} - 4 q^{42} - 8 q^{53} - 4 q^{64} - 8 q^{66} + 24 q^{68} + 20 q^{69} - 8 q^{72} - 4 q^{77} + 16 q^{81} - 4 q^{84} - 8 q^{93} + 24 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3332, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.1.be.a $6$ $1.663$ $$\Q(\zeta_{14})$$ $D_{7}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$-5$$ $$0$$ $$1$$ $$q+\zeta_{14}^{4}q^{2}+(-1+\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots$$
3332.1.be.b $6$ $1.663$ $$\Q(\zeta_{14})$$ $D_{7}$ $$\Q(\sqrt{-17})$$ None $$-1$$ $$5$$ $$0$$ $$-1$$ $$q+\zeta_{14}^{4}q^{2}+(1-\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots$$
3332.1.be.c $12$ $1.663$ $$\Q(\zeta_{28})$$ $D_{14}$ $$\Q(\sqrt{-17})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{28}^{8}q^{2}+(\zeta_{28}^{7}+\zeta_{28}^{13})q^{3}-\zeta_{28}^{2}q^{4}+\cdots$$