# Properties

 Label 128.3.d Level $128$ Weight $3$ Character orbit 128.d Rep. character $\chi_{128}(63,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $3$ Sturm bound $48$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 128.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## 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

 $$8q + 24q^{9} + O(q^{10})$$ $$8q + 24q^{9} + 16q^{17} + 8q^{25} - 32q^{33} - 176q^{41} - 120q^{49} - 32q^{57} - 64q^{65} + 464q^{73} + 360q^{81} - 48q^{89} + 528q^{97} + O(q^{100})$$

## 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.d.a $$2$$ $$3.488$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-9q^{9}+3iq^{13}+30q^{17}+\cdots$$
128.3.d.b $$2$$ $$3.488$$ $$\Q(\sqrt{2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+23q^{9}-3\beta q^{11}-2q^{17}+\cdots$$
128.3.d.c $$4$$ $$3.488$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(128, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 2}$$