# Properties

 Label 35.2.j Level $35$ Weight $2$ Character orbit 35.j Rep. character $\chi_{35}(4,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 35.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(35, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

## Trace form

 $$4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} + O(q^{10})$$ $$4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} - 4q^{10} + 8q^{14} + 8q^{15} + 2q^{16} + 12q^{19} + 4q^{20} - 10q^{21} + 6q^{24} + 6q^{25} - 4q^{26} - 28q^{29} + 2q^{30} - 4q^{31} - 8q^{34} - 16q^{35} + 8q^{36} - 4q^{39} - 12q^{40} + 20q^{41} - 4q^{45} + 6q^{46} + 26q^{49} + 16q^{50} + 4q^{51} + 10q^{54} + 6q^{56} + 20q^{59} - 4q^{60} - 14q^{61} - 28q^{64} + 8q^{65} - 12q^{69} - 10q^{70} - 8q^{71} - 16q^{74} - 8q^{75} - 24q^{76} - 4q^{79} + 2q^{80} - 2q^{81} + 8q^{84} + 16q^{85} - 14q^{86} + 18q^{89} + 16q^{90} - 4q^{91} + 12q^{95} + 10q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
35.2.j.a $$4$$ $$0.279$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$