# Properties

 Label 930.2.bn Level $930$ Weight $2$ Character orbit 930.bn Rep. character $\chi_{930}(19,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $256$ Newform subspaces $2$ 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.bn (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$2$$ 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 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

## Trace form

 $$256q + 64q^{4} - 16q^{6} - 32q^{9} + O(q^{10})$$ $$256q + 64q^{4} - 16q^{6} - 32q^{9} - 4q^{10} + 8q^{15} - 64q^{16} - 8q^{19} + 56q^{21} - 4q^{24} + 24q^{25} + 16q^{29} - 8q^{30} - 4q^{31} + 20q^{34} - 40q^{35} - 128q^{36} + 32q^{39} - 6q^{40} + 24q^{41} - 4q^{46} - 40q^{49} + 40q^{50} + 8q^{54} - 96q^{55} + 88q^{59} - 8q^{60} + 176q^{61} + 64q^{64} - 152q^{65} + 12q^{66} + 16q^{70} + 256q^{71} - 24q^{75} + 48q^{76} - 24q^{79} + 32q^{81} - 16q^{84} + 92q^{85} - 136q^{86} + 88q^{89} + 4q^{90} - 48q^{91} + 24q^{94} + 52q^{95} + 4q^{96} + O(q^{100})$$

## 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.bn.a $$112$$ $$7.426$$ None $$0$$ $$0$$ $$-2$$ $$0$$
930.2.bn.b $$144$$ $$7.426$$ None $$0$$ $$0$$ $$2$$ $$0$$

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

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