# Properties

 Label 648.1.bf Level $648$ Weight $1$ Character orbit 648.bf Rep. character $\chi_{648}(43,\cdot)$ Character field $\Q(\zeta_{54})$ Dimension $18$ Newform subspaces $1$ Sturm bound $108$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$648 = 2^{3} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 648.bf (of order $$54$$ and degree $$18$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$648$$ Character field: $$\Q(\zeta_{54})$$ Newform subspaces: $$1$$ Sturm bound: $$108$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(648, [\chi])$$.

Total New Old
Modular forms 54 54 0
Cusp forms 18 18 0
Eisenstein series 36 36 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 0 0 0

## Trace form

 $$18q + O(q^{10})$$ $$18q - 9q^{18} - 9q^{38} - 9q^{51} - 9q^{59} + 18q^{68} - 9q^{76} - 9q^{88} - 9q^{89} + 18q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(648, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
648.1.bf.a $$18$$ $$0.323$$ $$\Q(\zeta_{54})$$ $$D_{27}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots$$