# Properties

 Label 128.2.b Level $128$ Weight $2$ Character orbit 128.b Rep. character $\chi_{128}(65,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $32$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 128.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(128, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

## Trace form

 $$4 q - 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{9} + 8 q^{17} - 12 q^{25} - 16 q^{33} + 8 q^{41} - 28 q^{49} + 48 q^{57} + 32 q^{65} + 8 q^{73} + 20 q^{81} - 56 q^{89} - 56 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.2.b.a $2$ $1.022$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}-5q^{9}+\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots$$
128.2.b.b $2$ $1.022$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+3q^{9}-iq^{13}-2q^{17}-11q^{25}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

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