# Properties

 Label 30.2.c Level $30$ Weight $2$ Character orbit 30.c Rep. character $\chi_{30}(19,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$30 = 2 \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 30.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(30, [\chi])$$.

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

## Trace form

 $$2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{20} - 4 q^{21} - 2 q^{24} + 6 q^{25} - 12 q^{26} - 4 q^{30} - 16 q^{31} + 4 q^{34} + 4 q^{35} + 2 q^{36} + 12 q^{39} + 2 q^{40} + 4 q^{41} - 4 q^{44} + 4 q^{45} + 8 q^{46} + 6 q^{49} + 8 q^{50} - 4 q^{51} - 2 q^{54} - 8 q^{55} - 4 q^{56} - 20 q^{59} - 2 q^{60} + 4 q^{61} - 2 q^{64} - 12 q^{65} + 4 q^{66} - 8 q^{69} - 8 q^{70} + 24 q^{71} + 4 q^{74} - 8 q^{75} - 4 q^{80} + 2 q^{81} + 4 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{89} + 2 q^{90} + 24 q^{91} - 16 q^{94} + 2 q^{96} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(30, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
30.2.c.a $2$ $0.240$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots$$