# Properties

 Label 256.2.g Level $256$ Weight $2$ Character orbit 256.g Rep. character $\chi_{256}(33,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $24$ Newform subspaces $4$ Sturm bound $64$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$256 = 2^{8}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 256.g (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$4$$ Sturm bound: $$64$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(256, [\chi])$$.

Total New Old
Modular forms 160 40 120
Cusp forms 96 24 72
Eisenstein series 64 16 48

## Trace form

 $$24 q + 8 q^{5} - 8 q^{9} + O(q^{10})$$ $$24 q + 8 q^{5} - 8 q^{9} + 8 q^{13} + 8 q^{21} - 8 q^{25} + 8 q^{29} - 16 q^{33} + 8 q^{37} - 8 q^{41} - 16 q^{45} - 24 q^{53} - 8 q^{57} - 56 q^{61} - 16 q^{65} - 56 q^{69} - 8 q^{73} - 24 q^{77} - 32 q^{85} - 8 q^{89} + 32 q^{93} - 16 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(256, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.2.g.a $4$ $2.044$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$4$$ $$-4$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots$$
256.2.g.b $4$ $2.044$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$4$$ $$4$$ $$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
256.2.g.c $8$ $2.044$ 8.0.18939904.2 None $$0$$ $$-4$$ $$0$$ $$8$$ $$q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots$$
256.2.g.d $8$ $2.044$ 8.0.18939904.2 None $$0$$ $$4$$ $$0$$ $$-8$$ $$q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(256, [\chi])$$ into lower level spaces

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