# Properties

 Label 70.2.k Level $70$ Weight $2$ Character orbit 70.k Rep. character $\chi_{70}(3,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $16$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$70 = 2 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 70.k (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(70, [\chi])$$.

Total New Old
Modular forms 64 16 48
Cusp forms 32 16 16
Eisenstein series 32 0 32

## Trace form

 $$16 q - 12 q^{5} + 8 q^{7} + O(q^{10})$$ $$16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35} - 8 q^{36} + 4 q^{37} + 24 q^{38} + 36 q^{42} - 8 q^{43} - 12 q^{45} - 8 q^{46} + 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} - 4 q^{56} + 8 q^{57} - 32 q^{58} + 8 q^{60} - 12 q^{61} - 36 q^{63} - 8 q^{65} + 32 q^{67} - 36 q^{68} - 12 q^{70} + 16 q^{71} - 8 q^{72} - 12 q^{73} - 48 q^{75} + 16 q^{77} + 16 q^{78} - 12 q^{80} - 48 q^{82} + 24 q^{85} + 12 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{91} + 8 q^{92} + 28 q^{93} + 20 q^{95} + 12 q^{96} + 40 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(70, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.2.k.a $16$ $0.559$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$8$$ $$q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{4}+\beta _{13})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(70, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(70, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$