# Properties

 Label 128.2.g Level $128$ Weight $2$ Character orbit 128.g Rep. character $\chi_{128}(17,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $12$ Newform subspaces $2$ Sturm bound $32$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 128.g (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 80 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

## Trace form

 $$12 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10})$$ $$12 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 4 q^{23} - 4 q^{25} - 20 q^{27} - 4 q^{29} - 16 q^{31} - 8 q^{33} - 20 q^{35} - 4 q^{37} - 20 q^{39} - 4 q^{41} - 4 q^{43} + 8 q^{45} + 8 q^{51} + 12 q^{53} + 36 q^{55} - 4 q^{57} + 36 q^{59} + 28 q^{61} + 48 q^{63} - 8 q^{65} + 44 q^{67} + 28 q^{69} + 36 q^{71} - 4 q^{73} + 16 q^{75} + 12 q^{77} - 36 q^{83} + 16 q^{85} - 52 q^{87} - 4 q^{89} - 44 q^{91} - 16 q^{93} - 56 q^{95} - 8 q^{97} - 48 q^{99} + O(q^{100})$$

## 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.g.a $4$ $1.022$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$$
128.2.g.b $8$ $1.022$ 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 $$S_{2}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

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