# Properties

 Label 930.2.h Level $930$ Weight $2$ Character orbit 930.h Rep. character $\chi_{930}(371,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $4$ Sturm bound $384$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$93$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(930, [\chi])$$.

Total New Old
Modular forms 200 40 160
Cusp forms 184 40 144
Eisenstein series 16 0 16

## Trace form

 $$40q - 40q^{4} - 24q^{7} + O(q^{10})$$ $$40q - 40q^{4} - 24q^{7} + 40q^{16} + 16q^{18} + 24q^{19} - 40q^{25} + 24q^{28} + 16q^{31} + 8q^{33} - 8q^{39} + 8q^{45} - 16q^{51} + 8q^{63} - 40q^{64} - 16q^{66} + 72q^{67} + 16q^{69} - 16q^{72} - 24q^{76} + 24q^{78} - 24q^{81} - 16q^{82} - 32q^{87} - 16q^{90} + 16q^{93} + 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(930, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
930.2.h.a $$4$$ $$7.426$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$$
930.2.h.b $$4$$ $$7.426$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$$
930.2.h.c $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-20$$ $$q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$$
930.2.h.d $$16$$ $$7.426$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{6}q^{2}-\beta _{12}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{5}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(930, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(93, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(186, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$