# Properties

 Label 1200.1.z Level $1200$ Weight $1$ Character orbit 1200.z Rep. character $\chi_{1200}(107,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $2$ Sturm bound $240$ Trace bound $2$

# Related objects

## Defining parameters

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

## 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

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

## 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.z.a $2$ $0.599$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-15})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots$$
1200.1.z.b $2$ $0.599$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-15})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-iq^{3}+q^{4}-iq^{6}+q^{8}-q^{9}+\cdots$$