# Properties

 Label 256.2.b Level $256$ Weight $2$ Character orbit 256.b Rep. character $\chi_{256}(129,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $64$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$256 = 2^{8}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 256.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$64$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 44 10 34
Cusp forms 20 6 14
Eisenstein series 24 4 20

## Trace form

 $$6 q + 2 q^{9} + O(q^{10})$$ $$6 q + 2 q^{9} - 4 q^{17} + 6 q^{25} - 16 q^{33} + 4 q^{41} + 22 q^{49} - 16 q^{57} - 8 q^{65} - 44 q^{73} - 26 q^{81} - 12 q^{89} + 28 q^{97} + O(q^{100})$$

## 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.b.a $2$ $2.044$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots$$
256.2.b.b $2$ $2.044$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots$$
256.2.b.c $2$ $2.044$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots$$

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

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