# Properties

 Label 930.2.k Level $930$ Weight $2$ Character orbit 930.k Rep. character $\chi_{930}(247,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $64$ Newform subspaces $2$ Sturm bound $384$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$13$$

## 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

 $$64q - 8q^{7} + O(q^{10})$$ $$64q - 8q^{7} + 8q^{10} - 64q^{16} + 16q^{25} + 8q^{28} - 40q^{31} - 8q^{33} - 48q^{35} - 64q^{36} + 32q^{38} - 32q^{41} - 16q^{47} - 32q^{50} + 8q^{62} + 8q^{63} - 16q^{66} + 64q^{67} - 56q^{70} + 32q^{71} - 32q^{76} - 64q^{81} + 32q^{82} + 40q^{87} - 24q^{93} + 64q^{95} - 8q^{97} + 32q^{98} + O(q^{100})$$

## 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.k.a $$32$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$-4$$
930.2.k.b $$32$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$-4$$

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

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