# Properties

 Label 864.2.w Level 864 Weight 2 Character orbit w Rep. character $$\chi_{864}(107,\cdot)$$ 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.w (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$96$$ 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

 $$256q + O(q^{10})$$ $$256q - 8q^{10} + 64q^{16} - 16q^{22} + 32q^{40} + 32q^{46} + 56q^{52} + 32q^{55} + 32q^{58} - 32q^{61} + 48q^{64} - 128q^{67} + 48q^{70} - 64q^{76} + 32q^{79} - 40q^{82} - 40q^{88} + 48q^{91} - 72q^{94} + O(q^{100})$$

## 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.w.a $$128$$ $$6.899$$ None $$0$$ $$0$$ $$0$$ $$0$$
864.2.w.b $$128$$ $$6.899$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database