# Properties

 Label 930.2.bj Level $930$ Weight $2$ Character orbit 930.bj Rep. character $\chi_{930}(277,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $256$ Newform subspaces $2$ 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.bj (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ 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 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

## Trace form

 $$256q - 12q^{7} + O(q^{10})$$ $$256q - 12q^{7} - 8q^{10} + 64q^{16} + 80q^{21} + 20q^{22} - 16q^{25} - 8q^{28} + 40q^{31} + 8q^{33} + 48q^{35} - 256q^{36} - 32q^{38} - 48q^{41} + 20q^{42} + 40q^{46} + 96q^{47} - 48q^{50} + 80q^{53} + 80q^{55} - 8q^{62} - 8q^{63} + 120q^{65} - 24q^{66} - 64q^{67} + 56q^{70} + 48q^{71} + 80q^{73} - 48q^{76} + 40q^{77} + 64q^{81} - 32q^{82} - 200q^{85} - 40q^{87} - 80q^{91} - 16q^{93} + 16q^{95} + 128q^{97} - 32q^{98} + O(q^{100})$$

## 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.bj.a $$128$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$-16$$
930.2.bj.b $$128$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

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