# Properties

 Label 930.2.s Level $930$ Weight $2$ Character orbit 930.s Rep. character $\chi_{930}(439,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $4$ Sturm bound $384$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 400 64 336
Cusp forms 368 64 304
Eisenstein series 32 0 32

## Trace form

 $$64q - 64q^{4} - 4q^{6} + 32q^{9} + O(q^{10})$$ $$64q - 64q^{4} - 4q^{6} + 32q^{9} + 4q^{10} - 8q^{15} + 64q^{16} + 8q^{19} - 16q^{21} + 4q^{24} - 24q^{25} + 64q^{29} + 8q^{30} + 4q^{31} + 20q^{34} + 40q^{35} - 32q^{36} + 48q^{39} - 4q^{40} + 16q^{41} + 24q^{46} + 20q^{49} - 8q^{54} + 16q^{55} - 8q^{59} + 8q^{60} + 64q^{61} - 64q^{64} - 8q^{65} + 8q^{66} - 56q^{70} - 56q^{71} - 16q^{75} - 8q^{76} - 36q^{79} - 32q^{81} + 16q^{84} + 88q^{85} + 16q^{86} + 32q^{89} - 4q^{90} - 32q^{91} - 24q^{94} - 72q^{95} - 4q^{96} + O(q^{100})$$

## 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.s.a $$4$$ $$7.426$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots$$
930.2.s.b $$8$$ $$7.426$$ 8.0.49787136.1 None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{2}q^{3}-q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots$$
930.2.s.c $$24$$ $$7.426$$ None $$0$$ $$0$$ $$4$$ $$0$$
930.2.s.d $$28$$ $$7.426$$ None $$0$$ $$0$$ $$2$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(310, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$