# Properties

 Label 70.3.h Level $70$ Weight $3$ Character orbit 70.h Rep. character $\chi_{70}(19,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$70 = 2 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 70.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(70, [\chi])$$.

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

## Trace form

 $$16q + 16q^{4} - 6q^{5} - 12q^{9} + O(q^{10})$$ $$16q + 16q^{4} - 6q^{5} - 12q^{9} + 24q^{10} - 12q^{11} + 32q^{14} - 28q^{15} - 32q^{16} - 12q^{19} - 8q^{21} - 24q^{24} - 42q^{25} - 48q^{26} - 136q^{29} + 32q^{30} + 84q^{31} - 190q^{35} - 48q^{36} + 312q^{39} + 48q^{40} + 24q^{44} + 384q^{45} - 68q^{46} + 296q^{49} - 96q^{50} - 76q^{51} - 108q^{54} + 56q^{56} - 372q^{59} - 28q^{60} + 348q^{61} - 128q^{64} - 104q^{65} + 480q^{66} - 296q^{70} - 384q^{71} + 208q^{74} - 150q^{75} + 148q^{79} + 24q^{80} - 140q^{81} + 256q^{84} + 580q^{85} - 188q^{86} - 912q^{89} - 616q^{91} - 600q^{94} - 310q^{95} - 48q^{96} + 176q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(70, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
70.3.h.a $$16$$ $$1.907$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{10}q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(70, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(70, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$