# Properties

 Label 768.2.d Level $768$ Weight $2$ Character orbit 768.d Rep. character $\chi_{768}(385,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $8$ Sturm bound $256$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 768.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$256$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(768, [\chi])$$.

Total New Old
Modular forms 152 16 136
Cusp forms 104 16 88
Eisenstein series 48 0 48

## Trace form

 $$16q - 16q^{9} + O(q^{10})$$ $$16q - 16q^{9} - 16q^{25} - 16q^{49} + 32q^{57} - 32q^{65} + 64q^{73} + 16q^{81} + 32q^{89} - 32q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(768, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
768.2.d.a $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots$$
768.2.d.b $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+iq^{3}-2q^{7}-q^{9}-4iq^{11}-6iq^{13}+\cdots$$
768.2.d.c $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-iq^{3}+4iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots$$
768.2.d.d $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots$$
768.2.d.e $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots$$
768.2.d.f $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+iq^{3}+4iq^{5}+2q^{7}-q^{9}+4iq^{11}+\cdots$$
768.2.d.g $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-iq^{3}+2q^{7}-q^{9}+4iq^{11}-6iq^{13}+\cdots$$
768.2.d.h $$2$$ $$6.133$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-iq^{3}+2iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(768, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(768, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$