# Properties

 Label 3800.1.o Level $3800$ Weight $1$ Character orbit 3800.o Rep. character $\chi_{3800}(1101,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $7$ 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.o (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q$$ Newform subspaces: $$7$$ 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 40 28 12
Cusp forms 28 22 6
Eisenstein series 12 6 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 22 0 0 0

## Trace form

 $$22 q + 14 q^{4} - 2 q^{6} + 2 q^{7} + 20 q^{9} + O(q^{10})$$ $$22 q + 14 q^{4} - 2 q^{6} + 2 q^{7} + 20 q^{9} + 14 q^{16} + 2 q^{17} + 2 q^{23} - 10 q^{24} + 6 q^{26} + 2 q^{28} + 4 q^{36} - 2 q^{38} - 10 q^{39} - 2 q^{42} + 8 q^{44} - 4 q^{47} + 4 q^{49} - 2 q^{54} + 2 q^{57} + 2 q^{58} + 14 q^{64} + 8 q^{66} + 2 q^{68} + 2 q^{73} - 8 q^{74} + 18 q^{81} - 2 q^{87} + 2 q^{92} + 6 q^{96} + O(q^{100})$$

## 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.o.a $1$ $1.896$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$-1$$ $$1$$ $$0$$ $$1$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$$
3800.1.o.b $1$ $1.896$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$1$$ $$-1$$ $$0$$ $$1$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$$
3800.1.o.c $3$ $1.896$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-38})$$ None $$-3$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots$$
3800.1.o.d $3$ $1.896$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-38})$$ None $$-3$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots$$
3800.1.o.e $3$ $1.896$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-38})$$ None $$3$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots$$
3800.1.o.f $3$ $1.896$ $$\Q(\zeta_{18})^+$$ $D_{9}$ $$\Q(\sqrt{-38})$$ None $$3$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{6}+\cdots$$
3800.1.o.g $8$ $1.896$ $$\Q(\zeta_{16})$$ $D_{8}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}q^{2}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(3800, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(760, [\chi])$$$$^{\oplus 2}$$