# Properties

 Label 3800.1.b Level $3800$ Weight $1$ Character orbit 3800.b Rep. character $\chi_{3800}(949,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $600$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3800.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$600$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3800, [\chi])$$.

Total New Old
Modular forms 44 20 24
Cusp forms 32 16 16
Eisenstein series 12 4 8

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q - 16 q^{4} - 4 q^{6} - 12 q^{9} + O(q^{10})$$ $$16 q - 16 q^{4} - 4 q^{6} - 12 q^{9} + 16 q^{16} + 4 q^{24} - 4 q^{26} + 12 q^{36} + 8 q^{39} - 12 q^{49} + 8 q^{54} - 16 q^{64} + 4 q^{74} + 8 q^{81} - 4 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3800, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3800.1.b.a $2$ $1.896$ $$\Q(\sqrt{-1})$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots$$
3800.1.b.b $2$ $1.896$ $$\Q(\sqrt{-1})$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$$
3800.1.b.c $6$ $1.896$ 6.0.419904.1 $D_{9}$ $$\Q(\sqrt{-38})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{4}q^{6}+\beta _{1}q^{7}+\cdots$$
3800.1.b.d $6$ $1.896$ 6.0.419904.1 $D_{9}$ $$\Q(\sqrt{-38})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{5})q^{3}-q^{4}-\beta _{2}q^{6}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3800, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3800, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$