# Properties

 Label 930.2.bs Level $930$ Weight $2$ Character orbit 930.bs Rep. character $\chi_{930}(107,\cdot)$ Character field $\Q(\zeta_{60})$ Dimension $1024$ Newform subspaces $1$ Sturm bound $384$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.bs (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$465$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$384$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(930, [\chi])$$.

Total New Old
Modular forms 3200 1024 2176
Cusp forms 2944 1024 1920
Eisenstein series 256 0 256

## Trace form

 $$1024q - 8q^{3} + 24q^{7} + O(q^{10})$$ $$1024q - 8q^{3} + 24q^{7} + 8q^{10} + 8q^{12} - 8q^{15} + 256q^{16} + 44q^{22} + 16q^{25} - 20q^{27} + 4q^{28} + 48q^{30} - 32q^{31} - 52q^{33} + 112q^{37} + 12q^{42} + 40q^{45} + 24q^{46} - 12q^{48} + 16q^{51} - 20q^{55} - 40q^{57} - 56q^{58} - 12q^{60} + 32q^{61} + 224q^{63} - 32q^{66} + 24q^{67} - 24q^{70} - 88q^{73} + 224q^{75} - 96q^{76} - 32q^{78} + 48q^{81} - 24q^{85} + 20q^{87} - 36q^{88} + 8q^{90} - 80q^{91} - 252q^{93} - 32q^{97} + O(q^{100})$$

## 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.bs.a $$1024$$ $$7.426$$ None $$0$$ $$-8$$ $$0$$ $$24$$

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

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