# Properties

 Label 192.1.h Level $192$ Weight $1$ Character orbit 192.h Rep. character $\chi_{192}(161,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 192.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(192, [\chi])$$.

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

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

 $$2q - 2q^{9} + O(q^{10})$$ $$2q - 2q^{9} - 2q^{25} - 2q^{49} + 4q^{57} + 4q^{73} + 2q^{81} - 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(192, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
192.1.h.a $$2$$ $$0.096$$ $$\Q(\sqrt{-1})$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots$$