# Properties

 Label 1200.1.l Level $1200$ Weight $1$ Character orbit 1200.l Rep. character $\chi_{1200}(401,\cdot)$ Character field $\Q$ Dimension $2$ 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.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ 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 44 5 39
Cusp forms 8 2 6
Eisenstein series 36 3 33

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q + 2q^{9} + O(q^{10})$$ $$2q + 2q^{9} + 2q^{19} - 2q^{21} + 2q^{31} + 2q^{39} - 2q^{61} - 4q^{79} + 2q^{81} - 2q^{91} + O(q^{100})$$

## 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.l.a $$1$$ $$0.599$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $$q-q^{3}+q^{7}+q^{9}-q^{13}+q^{19}-q^{21}+\cdots$$
1200.1.l.b $$1$$ $$0.599$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+q^{3}-q^{7}+q^{9}+q^{13}+q^{19}-q^{21}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1200, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1200, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 3}$$