# Properties

 Label 256.6.b Level $256$ Weight $6$ Character orbit 256.b Rep. character $\chi_{256}(129,\cdot)$ Character field $\Q$ Dimension $38$ Newform subspaces $14$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$256 = 2^{8}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 256.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$14$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(256, [\chi])$$.

Total New Old
Modular forms 172 42 130
Cusp forms 148 38 110
Eisenstein series 24 4 20

## Trace form

 $$38 q - 2750 q^{9} + O(q^{10})$$ $$38 q - 2750 q^{9} - 4 q^{17} - 18746 q^{25} - 976 q^{33} + 4 q^{41} + 120950 q^{49} + 52528 q^{57} + 42872 q^{65} + 230420 q^{73} + 143366 q^{81} + 140468 q^{89} - 294756 q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(256, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.6.b.a $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-488$$ $$q+3iq^{3}+47iq^{5}-244q^{7}+207q^{9}+\cdots$$
256.6.b.b $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-416$$ $$q+4iq^{3}-7iq^{5}-208q^{7}+179q^{9}+\cdots$$
256.6.b.c $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-176$$ $$q+6iq^{3}-3^{3}iq^{5}-88q^{7}+99q^{9}+\cdots$$
256.6.b.d $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-48$$ $$q+10iq^{3}-37iq^{5}-24q^{7}-157q^{9}+\cdots$$
256.6.b.e $2$ $41.058$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-41iq^{5}+3^{5}q^{9}+597iq^{13}+2242q^{17}+\cdots$$
256.6.b.f $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$48$$ $$q+10iq^{3}+37iq^{5}+24q^{7}-157q^{9}+\cdots$$
256.6.b.g $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$176$$ $$q+6iq^{3}+3^{3}iq^{5}+88q^{7}+99q^{9}+\cdots$$
256.6.b.h $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$416$$ $$q+4iq^{3}+7iq^{5}+208q^{7}+179q^{9}+\cdots$$
256.6.b.i $2$ $41.058$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$488$$ $$q+3iq^{3}-47iq^{5}+244q^{7}+207q^{9}+\cdots$$
256.6.b.j $4$ $41.058$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$-368$$ $$q+(\beta _{1}+\beta _{2})q^{3}+(-5^{2}\beta _{1}+2\beta _{2})q^{5}+\cdots$$
256.6.b.k $4$ $41.058$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$-272$$ $$q+(-5\beta _{1}+\beta _{3})q^{3}+(11\beta _{1}-2\beta _{3})q^{5}+\cdots$$
256.6.b.l $4$ $41.058$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{3}-23\zeta_{12}q^{5}+3\zeta_{12}^{3}q^{7}+\cdots$$
256.6.b.m $4$ $41.058$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$0$$ $$272$$ $$q+(-5\beta _{1}+\beta _{3})q^{3}+(-11\beta _{1}+2\beta _{3})q^{5}+\cdots$$
256.6.b.n $4$ $41.058$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$368$$ $$q+(\beta _{1}+\beta _{2})q^{3}+(5^{2}\beta _{1}-2\beta _{2})q^{5}+(92+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(256, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(256, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$