# Properties

 Label 50.2.b Level $50$ Weight $2$ Character orbit 50.b Rep. character $\chi_{50}(49,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $15$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$50 = 2 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 50.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$15$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(50, [\chi])$$.

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

## Trace form

 $$2q - 2q^{4} - 2q^{6} + 4q^{9} + O(q^{10})$$ $$2q - 2q^{4} - 2q^{6} + 4q^{9} - 6q^{11} + 4q^{14} + 2q^{16} - 10q^{19} + 4q^{21} + 2q^{24} + 8q^{26} + 4q^{31} - 6q^{34} - 4q^{36} + 8q^{39} - 6q^{41} + 6q^{44} - 12q^{46} + 6q^{49} - 6q^{51} - 10q^{54} - 4q^{56} + 4q^{61} - 2q^{64} + 6q^{66} - 12q^{69} + 24q^{71} + 4q^{74} + 10q^{76} + 20q^{79} + 2q^{81} - 4q^{84} + 8q^{86} - 30q^{89} - 16q^{91} + 24q^{94} - 2q^{96} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(50, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
50.2.b.a $$2$$ $$0.399$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots$$