# Properties

 Label 35.2.f Level $35$ Weight $2$ Character orbit 35.f Rep. character $\chi_{35}(13,\cdot)$ Character field $\Q(\zeta_{4})$ 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.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(i)$$ 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

 $$4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} + O(q^{10})$$ $$4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} - 4 q^{11} + 16 q^{16} + 8 q^{18} - 20 q^{21} + 4 q^{22} + 8 q^{23} - 20 q^{30} + 20 q^{35} - 24 q^{37} + 20 q^{42} - 12 q^{43} - 16 q^{46} + 20 q^{50} + 20 q^{51} + 4 q^{53} - 16 q^{56} + 20 q^{57} + 12 q^{58} - 8 q^{63} - 4 q^{67} - 20 q^{70} - 24 q^{71} - 16 q^{72} - 4 q^{77} - 20 q^{78} + 44 q^{81} - 20 q^{85} + 24 q^{86} + 8 q^{88} + 20 q^{91} + 20 q^{93} - 20 q^{95} - 12 q^{98} + O(q^{100})$$

## 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.f.a $4$ $0.279$ $$\Q(i, \sqrt{10})$$ None $$-4$$ $$0$$ $$0$$ $$4$$ $$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$$