# Properties

 Label 832.2.w Level $832$ Weight $2$ Character orbit 832.w Rep. character $\chi_{832}(257,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $52$ Newform subspaces $10$ Sturm bound $224$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$832 = 2^{6} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 832.w (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$224$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(832, [\chi])$$.

Total New Old
Modular forms 248 60 188
Cusp forms 200 52 148
Eisenstein series 48 8 40

## Trace form

 $$52 q - 24 q^{9} + O(q^{10})$$ $$52 q - 24 q^{9} - 4 q^{13} - 6 q^{17} - 52 q^{25} + 2 q^{29} - 6 q^{33} + 6 q^{37} + 6 q^{41} - 24 q^{45} + 12 q^{49} + 8 q^{53} + 10 q^{61} + 20 q^{65} - 10 q^{69} + 36 q^{77} - 18 q^{81} - 24 q^{85} - 6 q^{89} + 12 q^{93} - 6 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(832, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
832.2.w.a $2$ $6.644$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+\cdots$$
832.2.w.b $2$ $6.644$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-3$$ $$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$$
832.2.w.c $2$ $6.644$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$3$$ $$q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$$
832.2.w.d $2$ $6.644$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$$
832.2.w.e $4$ $6.644$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2-4\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
832.2.w.f $4$ $6.644$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-1+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+3\zeta_{12}^{2}q^{9}+\cdots$$
832.2.w.g $8$ $6.644$ 8.0.195105024.2 None $$0$$ $$-2$$ $$0$$ $$-6$$ $$q+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$$
832.2.w.h $8$ $6.644$ 8.0.56070144.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+(\beta _{4}-\beta _{5})q^{5}-\beta _{3}q^{7}+(-2+\cdots)q^{9}+\cdots$$
832.2.w.i $8$ $6.644$ 8.0.195105024.2 None $$0$$ $$2$$ $$0$$ $$6$$ $$q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
832.2.w.j $12$ $6.644$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+(2\beta _{4}+\beta _{5}-\beta _{6})q^{5}+\beta _{3}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(832, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(832, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(416, [\chi])$$$$^{\oplus 2}$$