# Properties

 Label 140.1.h Level $140$ Weight $1$ Character orbit 140.h Rep. character $\chi_{140}(69,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $24$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 140.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(140, [\chi])$$.

Total New Old
Modular forms 8 2 6
Cusp forms 2 2 0
Eisenstein series 6 0 6

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

 $$2 q + O(q^{10})$$ $$2 q - 2 q^{11} - 2 q^{15} - 2 q^{21} + 2 q^{25} - 2 q^{29} + 2 q^{35} + 2 q^{39} + 2 q^{49} + 2 q^{51} - 2 q^{65} + 4 q^{71} - 2 q^{79} - 2 q^{81} - 2 q^{85} - 2 q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(140, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
140.1.h.a $1$ $0.070$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-35})$$ None $$0$$ $$-1$$ $$1$$ $$1$$ $$q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots$$
140.1.h.b $1$ $0.070$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-35})$$ None $$0$$ $$1$$ $$-1$$ $$-1$$ $$q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots$$