# Properties

 Label 930.2.bt Level $930$ Weight $2$ Character orbit 930.bt Rep. character $\chi_{930}(13,\cdot)$ Character field $\Q(\zeta_{60})$ Dimension $512$ 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.bt (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$155$$ Character field: $$\Q(\zeta_{60})$$ 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 3200 512 2688
Cusp forms 2944 512 2432
Eisenstein series 256 0 256

## Trace form

 $$512q + 24q^{7} + O(q^{10})$$ $$512q + 24q^{7} + 8q^{10} + 128q^{16} - 32q^{21} + 52q^{22} - 8q^{25} - 4q^{28} - 16q^{31} - 8q^{33} - 48q^{35} + 256q^{36} - 72q^{37} + 32q^{38} + 96q^{41} + 28q^{42} + 96q^{43} - 40q^{46} - 96q^{47} + 96q^{50} - 80q^{53} + 100q^{55} + 24q^{57} - 16q^{62} + 8q^{63} + 96q^{65} + 24q^{66} - 32q^{67} + 88q^{70} - 96q^{71} - 32q^{73} + 96q^{76} - 40q^{77} - 64q^{81} - 16q^{82} + 24q^{83} + 200q^{85} + 48q^{86} + 52q^{87} + 108q^{88} + 80q^{91} + 16q^{93} - 208q^{95} + 16q^{97} + 32q^{98} + O(q^{100})$$

## 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.bt.a $$256$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$8$$
930.2.bt.b $$256$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$16$$

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

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