# Properties

 Label 30.3.d Level $30$ Weight $3$ Character orbit 30.d Rep. character $\chi_{30}(11,\cdot)$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ 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

 $$4q + 4q^{3} - 8q^{4} - 4q^{6} + 8q^{7} - 8q^{9} + O(q^{10})$$ $$4q + 4q^{3} - 8q^{4} - 4q^{6} + 8q^{7} - 8q^{9} - 8q^{12} - 40q^{13} + 20q^{15} + 16q^{16} + 32q^{18} + 32q^{19} - 52q^{21} + 48q^{22} + 8q^{24} - 20q^{25} + 28q^{27} - 16q^{28} - 20q^{30} + 32q^{31} + 24q^{33} - 96q^{34} + 16q^{36} - 88q^{37} - 40q^{39} - 128q^{42} + 56q^{43} + 20q^{45} - 24q^{46} + 16q^{48} + 180q^{49} + 72q^{51} + 80q^{52} + 140q^{54} + 152q^{57} - 40q^{60} - 64q^{61} - 256q^{63} - 32q^{64} + 48q^{66} - 328q^{67} - 132q^{69} + 120q^{70} - 64q^{72} + 200q^{73} - 20q^{75} - 64q^{76} + 40q^{78} - 112q^{79} + 28q^{81} + 192q^{82} + 104q^{84} - 120q^{85} + 240q^{87} - 96q^{88} - 80q^{90} - 80q^{91} + 32q^{93} - 120q^{94} - 16q^{96} + 296q^{97} - 192q^{99} + O(q^{100})$$

## 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.d.a $$4$$ $$0.817$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$8$$ $$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots$$

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

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