# Properties

 Label 79.1.b Level $79$ Weight $1$ Character orbit 79.b Rep. character $\chi_{79}(78,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$79$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 79.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$79$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(79, [\chi])$$.

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 0
Eisenstein series 1 1 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

 $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{8} + 2 q^{9} + O(q^{10})$$ $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{8} + 2 q^{9} - 2 q^{10} - q^{11} - q^{13} - q^{18} - q^{19} + 2 q^{20} + 3 q^{22} - q^{23} + q^{25} + 3 q^{26} - q^{31} + 2 q^{32} + q^{36} - 2 q^{38} + q^{40} - 3 q^{44} - q^{45} - 2 q^{46} + 2 q^{49} + 2 q^{50} - 3 q^{52} - 2 q^{55} + 3 q^{62} - q^{64} - 2 q^{65} - q^{67} - 2 q^{72} - q^{73} + 2 q^{76} + 2 q^{79} + 2 q^{81} + 4 q^{83} + q^{88} - q^{89} - 2 q^{90} + 2 q^{92} + 3 q^{95} - q^{97} - q^{98} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(79, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
79.1.b.a $2$ $0.039$ $$\Q(\sqrt{5})$$ $D_{5}$ $$\Q(\sqrt{-79})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$$