# Properties

 Label 3267.1.bf Level $3267$ Weight $1$ Character orbit 3267.bf Rep. character $\chi_{3267}(40,\cdot)$ Character field $\Q(\zeta_{90})$ Dimension $24$ Newform subspaces $1$ Sturm bound $396$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3267 = 3^{3} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3267.bf (of order $$90$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$297$$ Character field: $$\Q(\zeta_{90})$$ Newform subspaces: $$1$$ Sturm bound: $$396$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3267, [\chi])$$.

Total New Old
Modular forms 312 216 96
Cusp forms 24 24 0
Eisenstein series 288 192 96

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24 q + 3 q^{5} + O(q^{10})$$ $$24 q + 3 q^{5} + 3 q^{15} - 6 q^{20} + 3 q^{25} + 3 q^{27} + 3 q^{31} - 6 q^{36} + 3 q^{47} + 3 q^{48} + 3 q^{59} + 3 q^{64} + 24 q^{67} - 6 q^{75} + 12 q^{89} - 6 q^{93} - 6 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3267, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3267.1.bf.a $24$ $1.630$ $$\Q(\zeta_{45})$$ $D_{9}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+\zeta_{90}^{34}q^{3}-\zeta_{90}^{31}q^{4}+(\zeta_{90}^{32}+\cdots)q^{5}+\cdots$$