# Properties

 Label 930.2.br Level $930$ Weight $2$ Character orbit 930.br Rep. character $\chi_{930}(11,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $352$ Newform subspaces $2$ Sturm bound $384$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.br (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$93$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$9$$ 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 352 1248
Cusp forms 1472 352 1120
Eisenstein series 128 0 128

## Trace form

 $$352q + 88q^{4} + 8q^{7} + O(q^{10})$$ $$352q + 88q^{4} + 8q^{7} - 88q^{16} + 16q^{18} + 16q^{19} - 60q^{21} + 176q^{25} - 60q^{27} + 72q^{28} + 56q^{31} - 52q^{33} + 28q^{34} + 16q^{39} - 24q^{42} - 80q^{43} + 8q^{45} + 20q^{46} + 60q^{49} + 64q^{51} + 8q^{55} + 192q^{57} - 40q^{58} + 48q^{63} + 88q^{64} - 8q^{66} - 56q^{67} + 164q^{69} - 16q^{72} - 80q^{73} + 24q^{76} - 32q^{78} - 48q^{79} - 232q^{81} - 72q^{82} - 20q^{84} - 8q^{87} + 48q^{90} - 160q^{91} - 132q^{93} - 56q^{94} - 24q^{97} - 192q^{99} + O(q^{100})$$

## 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.br.a $$176$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$4$$
930.2.br.b $$176$$ $$7.426$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

$$S_{2}^{\mathrm{old}}(930, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(93, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(186, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 2}$$