# Properties

 Label 34.2.b Level $34$ Weight $2$ Character orbit 34.b Rep. character $\chi_{34}(33,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $9$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$34 = 2 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 34.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(34, [\chi])$$.

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

## Trace form

 $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 10 q^{9} + O(q^{10})$$ $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 10 q^{9} + 4 q^{13} + 16 q^{15} + 2 q^{16} - 6 q^{17} + 10 q^{18} - 8 q^{19} - 6 q^{25} - 4 q^{26} - 16 q^{30} - 2 q^{32} + 16 q^{33} + 6 q^{34} - 10 q^{36} + 8 q^{38} - 8 q^{43} + 14 q^{49} + 6 q^{50} - 16 q^{51} + 4 q^{52} + 12 q^{53} - 16 q^{55} + 24 q^{59} + 16 q^{60} + 2 q^{64} - 16 q^{66} - 8 q^{67} - 6 q^{68} - 32 q^{69} + 10 q^{72} - 8 q^{76} + 2 q^{81} - 24 q^{83} + 16 q^{85} + 8 q^{86} + 16 q^{87} + 12 q^{89} - 14 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(34, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
34.2.b.a $2$ $0.271$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots$$