# Properties

 Label 1200.1.bd Level $1200$ Weight $1$ Character orbit 1200.bd Rep. character $\chi_{1200}(443,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $2$ Sturm bound $240$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1200.bd (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$240$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$240$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1200, [\chi])$$.

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
Eisenstein series 24 8 16

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

 $$4q - 4q^{4} + 4q^{9} + O(q^{10})$$ $$4q - 4q^{4} + 4q^{9} + 4q^{16} + 4q^{19} - 4q^{34} - 4q^{36} - 4q^{46} - 4q^{51} - 4q^{61} - 4q^{64} + 4q^{69} - 4q^{76} + 4q^{81} + 4q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1200, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1200.1.bd.a $$2$$ $$0.599$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{8}+q^{9}+\cdots$$
1200.1.bd.b $$2$$ $$0.599$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots$$