# Properties

 Label 35.2.k Level $35$ Weight $2$ Character orbit 35.k Rep. character $\chi_{35}(3,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $8$ Newform subspaces $2$ Sturm bound $8$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 35.k (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$8$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

## Trace form

 $$8q - 2q^{2} - 6q^{3} - 10q^{7} - 4q^{8} + O(q^{10})$$ $$8q - 2q^{2} - 6q^{3} - 10q^{7} - 4q^{8} + 6q^{10} + 4q^{11} + 6q^{12} - 12q^{15} - 4q^{16} + 12q^{17} + 4q^{18} + 20q^{21} + 8q^{22} + 10q^{23} - 12q^{25} - 24q^{26} + 18q^{28} + 8q^{30} - 24q^{31} - 18q^{32} - 8q^{35} - 24q^{36} - 12q^{38} + 18q^{40} - 26q^{42} - 12q^{43} + 24q^{45} + 28q^{46} + 24q^{47} + 28q^{50} - 8q^{51} + 24q^{52} + 20q^{53} + 16q^{56} + 16q^{57} - 6q^{58} - 6q^{60} - 24q^{61} - 4q^{63} - 24q^{65} - 12q^{66} - 14q^{67} - 12q^{68} - 40q^{70} + 24q^{71} - 8q^{72} - 24q^{73} - 6q^{75} - 20q^{77} + 32q^{78} - 24q^{80} - 8q^{81} - 6q^{82} + 8q^{85} + 36q^{86} + 18q^{87} - 8q^{88} + 40q^{91} - 36q^{92} + 4q^{93} + 8q^{95} + 60q^{96} + 18q^{98} + O(q^{100})$$

## 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.k.a $$4$$ $$0.279$$ $$\Q(\zeta_{12})$$ None $$-4$$ $$-2$$ $$-4$$ $$0$$ $$q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$$
35.2.k.b $$4$$ $$0.279$$ $$\Q(\zeta_{12})$$ None $$2$$ $$-4$$ $$4$$ $$-10$$ $$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$$