# Properties

 Label 56.2.b Level $56$ Weight $2$ Character orbit 56.b Rep. character $\chi_{56}(29,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$56 = 2^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 56.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(56, [\chi])$$.

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

## Trace form

 $$6q - q^{2} - 3q^{4} + 2q^{6} - 2q^{7} - 7q^{8} - 6q^{9} + O(q^{10})$$ $$6q - q^{2} - 3q^{4} + 2q^{6} - 2q^{7} - 7q^{8} - 6q^{9} - 4q^{10} + 14q^{12} + q^{14} + 8q^{15} + q^{16} - 4q^{17} - 15q^{18} + 4q^{20} - 6q^{22} - 8q^{23} + 6q^{24} - 2q^{25} + 20q^{26} - 5q^{28} + 16q^{30} - 16q^{31} + 9q^{32} + 8q^{33} - 2q^{34} + 11q^{36} + 18q^{38} + 8q^{39} - 28q^{40} - 4q^{41} - 10q^{42} - 18q^{44} + 16q^{46} - 10q^{48} + 6q^{49} + 19q^{50} - 4q^{52} - 44q^{54} + 32q^{55} + 7q^{56} - 8q^{57} - 20q^{58} - 24q^{60} - 32q^{62} + 10q^{63} - 15q^{64} + 16q^{65} - 4q^{66} + 26q^{68} + 12q^{70} - 32q^{71} + 31q^{72} - 20q^{73} - 12q^{74} + 14q^{76} - 16q^{78} + 16q^{79} + 36q^{80} + 14q^{81} + 38q^{82} - 14q^{84} + 26q^{86} + 32q^{87} + 38q^{88} - 20q^{89} + 20q^{90} + 8q^{92} - 8q^{95} - 58q^{96} - 4q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(56, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
56.2.b.a $$2$$ $$0.447$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots$$
56.2.b.b $$4$$ $$0.447$$ 4.0.2312.1 None $$-1$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$