# Properties

 Label 3800.1.cv Level $3800$ Weight $1$ Character orbit 3800.cv Rep. character $\chi_{3800}(251,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $42$ Newform subspaces $6$ Sturm bound $600$ Trace bound $22$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3800.cv (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$6$$ Sturm bound: $$600$$ Trace bound: $$22$$

## Dimensions

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

Total New Old
Modular forms 132 78 54
Cusp forms 60 42 18
Eisenstein series 72 36 36

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 42 0 0 0

## Trace form

 $$42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} + O(q^{10})$$ $$42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 12 q^{14} - 6 q^{18} - 6 q^{22} + 3 q^{24} + 6 q^{26} - 3 q^{27} + 3 q^{33} + 3 q^{36} + 3 q^{38} - 3 q^{41} - 6 q^{48} - 9 q^{49} - 21 q^{51} + 3 q^{54} - 15 q^{59} - 9 q^{64} - 15 q^{66} + 3 q^{67} - 3 q^{68} - 6 q^{72} - 6 q^{73} + 6 q^{74} - 6 q^{76} - 3 q^{81} + 3 q^{82} - 12 q^{89} - 12 q^{91} + 12 q^{94} + 3 q^{97} + 39 q^{99} + O(q^{100})$$

## 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.cv.a $6$ $1.896$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$$
3800.1.cv.b $6$ $1.896$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-3$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$$
3800.1.cv.c $6$ $1.896$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots$$
3800.1.cv.d $6$ $1.896$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$3$$ $$0$$ $$0$$ $$q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$$
3800.1.cv.e $6$ $1.896$ $$\Q(\zeta_{18})$$ $D_{9}$ $$\Q(\sqrt{-2})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$$
3800.1.cv.f $12$ $1.896$ $$\Q(\zeta_{36})$$ $D_{9}$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}^{13}-\zeta_{36}^{17}+\cdots)q^{7}+\cdots$$

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

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