# Properties

 Label 56.1.h Level $56$ Weight $1$ Character orbit 56.h Rep. character $\chi_{56}(13,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$56 = 2^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 56.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(56, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 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 1 0 0 0

## Trace form

 $$q - q^{2} + q^{4} - q^{7} - q^{8} - q^{9} + O(q^{10})$$ $$q - q^{2} + q^{4} - q^{7} - q^{8} - q^{9} + q^{14} + q^{16} + q^{18} + 2q^{23} - q^{25} - q^{28} - q^{32} - q^{36} - 2q^{46} + q^{49} + q^{50} + q^{56} + q^{63} + q^{64} - 2q^{71} + q^{72} - 2q^{79} + q^{81} + 2q^{92} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(56, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
56.1.h.a $$1$$ $$0.028$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-14})$$ $$\Q(\sqrt{2})$$ $$-1$$ $$0$$ $$0$$ $$-1$$ $$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$$