# Properties

 Label 1600.1.b Level $1600$ Weight $1$ Character orbit 1600.b Rep. character $\chi_{1600}(1151,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $240$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1600.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$240$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1600, [\chi])$$.

Total New Old
Modular forms 40 4 36
Cusp forms 4 1 3
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 1 0 0 0

## Trace form

 $$q + q^{9} + O(q^{10})$$ $$q + q^{9} + 2 q^{29} - 2 q^{41} + q^{49} + 2 q^{61} + q^{81} - 2 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1600, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.1.b.a $1$ $0.799$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{9}+2q^{29}-2q^{41}+q^{49}+2q^{61}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1600, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1600, [\chi]) \cong$$