# Properties

 Label 35.3.c Level $35$ Weight $3$ Character orbit 35.c Rep. character $\chi_{35}(34,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $12$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 35.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$12$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(35, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q - 12q^{4} - 12q^{9} + O(q^{10})$$ $$6q - 12q^{4} - 12q^{9} + 30q^{11} + 36q^{14} - 30q^{15} - 12q^{16} - 66q^{21} - 30q^{25} + 102q^{29} + 180q^{30} - 30q^{35} - 84q^{36} - 78q^{39} - 384q^{44} + 144q^{46} + 222q^{49} - 180q^{50} + 138q^{51} - 36q^{56} + 60q^{60} + 492q^{64} + 210q^{65} - 360q^{70} - 60q^{71} - 216q^{74} - 618q^{79} - 246q^{81} + 456q^{84} - 330q^{85} + 504q^{86} - 186q^{91} + 540q^{95} + 264q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
35.3.c.a $$1$$ $$0.954$$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$-1$$ $$5$$ $$-7$$ $$q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots$$
35.3.c.b $$1$$ $$0.954$$ $$\Q$$ $$\Q(\sqrt{-35})$$ $$0$$ $$1$$ $$-5$$ $$7$$ $$q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots$$
35.3.c.c $$4$$ $$0.954$$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$$