# Properties

 Label 3267.1.l Level $3267$ Weight $1$ Character orbit 3267.l Rep. character $\chi_{3267}(838,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $16$ Newform subspaces $1$ Sturm bound $396$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$3267 = 3^{3} \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3267.l (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{10})$$ 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 176 16 160
Cusp forms 32 16 16
Eisenstein series 144 0 144

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q - 4 q^{4} + O(q^{10})$$ $$16 q - 4 q^{4} - 4 q^{16} + 4 q^{25} + 4 q^{49} - 4 q^{64} + 4 q^{91} - 4 q^{97} + O(q^{100})$$

## 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.l.a $16$ $1.630$ 16.0.$$\cdots$$.7 $D_{12}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{4}-\beta _{12}q^{7}+\beta _{3}q^{13}-\beta _{8}q^{16}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3267, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3267, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(1089, [\chi])$$$$^{\oplus 2}$$