# Properties

 Label 441.1.q Level $441$ Weight $1$ Character orbit 441.q Rep. character $\chi_{441}(116,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $56$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 441.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(441, [\chi])$$.

Total New Old
Modular forms 36 4 32
Cusp forms 4 4 0
Eisenstein series 32 0 32

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4q + 2q^{4} + O(q^{10})$$ $$4q + 2q^{4} + 2q^{16} - 8q^{22} - 2q^{25} - 4q^{46} - 4q^{58} + 4q^{64} + 4q^{67} - 4q^{79} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(441, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
441.1.q.a $$4$$ $$0.220$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$$