# Properties

 Label 864.2.v Level $864$ Weight $2$ Character orbit 864.v Rep. character $\chi_{864}(109,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $256$ Newform subspaces $2$ Sturm bound $288$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 864.v (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(864, [\chi])$$.

Total New Old
Modular forms 600 256 344
Cusp forms 552 256 296
Eisenstein series 48 0 48

## Trace form

 $$256 q + O(q^{10})$$ $$256 q + 8 q^{10} - 64 q^{16} + 16 q^{22} + 32 q^{40} + 32 q^{46} + 8 q^{52} - 32 q^{55} + 32 q^{58} + 32 q^{61} - 48 q^{64} + 128 q^{67} - 48 q^{70} + 64 q^{76} - 40 q^{82} - 40 q^{88} + 48 q^{91} - 24 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(864, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.2.v.a $128$ $6.899$ None $$0$$ $$0$$ $$0$$ $$0$$
864.2.v.b $128$ $6.899$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(864, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(864, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$