# Properties

 Label 300.1.b Level $300$ Weight $1$ Character orbit 300.b Rep. character $\chi_{300}(149,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 300.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(300, [\chi])$$.

Total New Old
Modular forms 20 2 18
Cusp forms 2 2 0
Eisenstein series 18 0 18

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q - 2q^{9} + O(q^{10})$$ $$2q - 2q^{9} + 2q^{19} - 2q^{21} - 2q^{31} + 2q^{39} - 2q^{61} - 4q^{79} + 2q^{81} + 2q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(300, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
300.1.b.a $$2$$ $$0.150$$ $$\Q(\sqrt{-1})$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots$$