# Properties

 Label 70.2.c Level $70$ Weight $2$ Character orbit 70.c Rep. character $\chi_{70}(29,\cdot)$ Character field $\Q$ Dimension $4$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ 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 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

## Trace form

 $$4q - 4q^{4} + 4q^{5} - 12q^{9} + O(q^{10})$$ $$4q - 4q^{4} + 4q^{5} - 12q^{9} + 4q^{10} - 4q^{14} + 12q^{15} + 4q^{16} - 16q^{19} - 4q^{20} - 8q^{26} - 8q^{29} + 12q^{30} + 16q^{31} + 8q^{34} + 4q^{35} + 12q^{36} + 24q^{39} - 4q^{40} - 24q^{41} - 12q^{45} + 8q^{46} - 4q^{49} - 4q^{50} - 24q^{55} + 4q^{56} + 16q^{59} - 12q^{60} + 24q^{61} - 4q^{64} - 4q^{65} - 48q^{66} + 48q^{69} - 4q^{70} - 24q^{71} + 8q^{74} + 16q^{76} - 8q^{79} + 4q^{80} - 36q^{81} - 8q^{85} - 16q^{86} + 40q^{89} - 12q^{90} - 8q^{91} + 16q^{94} - 4q^{95} + O(q^{100})$$

## 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.c.a $$4$$ $$0.559$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$$

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

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