# Properties

 Label 30.3.b Level $30$ Weight $3$ Character orbit 30.b Rep. character $\chi_{30}(29,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$30 = 2 \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 30.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(30, [\chi])$$.

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

## Trace form

 $$4q + 8q^{4} - 4q^{6} - 32q^{9} + O(q^{10})$$ $$4q + 8q^{4} - 4q^{6} - 32q^{9} - 16q^{10} + 8q^{15} + 16q^{16} + 48q^{19} + 68q^{21} - 8q^{24} - 36q^{25} + 68q^{30} - 128q^{31} - 64q^{34} - 64q^{36} - 32q^{40} - 68q^{45} + 136q^{46} + 60q^{49} + 32q^{51} + 100q^{54} + 272q^{55} + 16q^{60} - 64q^{61} + 32q^{64} - 272q^{66} - 68q^{69} - 136q^{70} - 272q^{75} + 96q^{76} - 288q^{79} + 188q^{81} + 136q^{84} + 128q^{85} + 128q^{90} - 200q^{94} - 16q^{96} + 272q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(30, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
30.3.b.a $$4$$ $$0.817$$ $$\Q(\sqrt{2}, \sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(30, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(30, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 2}$$