# Properties

 Label 152.1.g Level $152$ Weight $1$ Character orbit 152.g Rep. character $\chi_{152}(37,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $20$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 152.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(152, [\chi])$$.

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

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

 $$2 q + 2 q^{4} - 2 q^{6} - 2 q^{7} + O(q^{10})$$ $$2 q + 2 q^{4} - 2 q^{6} - 2 q^{7} + 2 q^{16} - 2 q^{17} - 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{28} + 2 q^{38} + 2 q^{39} + 2 q^{42} + 4 q^{47} + 2 q^{54} - 2 q^{57} - 2 q^{58} + 2 q^{64} - 2 q^{68} - 2 q^{73} + 4 q^{74} - 2 q^{81} + 2 q^{87} - 2 q^{92} - 2 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(152, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.1.g.a $1$ $0.076$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$-1$$ $$1$$ $$0$$ $$-1$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$$
152.1.g.b $1$ $0.076$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-38})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$$