# Properties

 Label 128.3.c Level $128$ Weight $3$ Character orbit 128.c Rep. character $\chi_{128}(127,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $48$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 128.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(128, [\chi])$$.

Total New Old
Modular forms 40 8 32
Cusp forms 24 8 16
Eisenstein series 16 0 16

## Trace form

 $$8q - 24q^{9} + O(q^{10})$$ $$8q - 24q^{9} - 16q^{17} + 88q^{25} - 32q^{33} + 16q^{41} + 8q^{49} - 352q^{57} + 160q^{65} + 176q^{73} + 232q^{81} + 432q^{89} - 656q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(128, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
128.3.c.a $$4$$ $$3.488$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\zeta_{8}q^{3}+(-2-\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$$
128.3.c.b $$4$$ $$3.488$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{8}q^{3}+(2+\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(128, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(128, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$