# Properties

 Label 462.2.ba Level $462$ Weight $2$ Character orbit 462.ba Rep. character $\chi_{462}(19,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $128$ Newform subspaces $2$ Sturm bound $192$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.ba (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$2$$ Sturm bound: $$192$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(462, [\chi])$$.

Total New Old
Modular forms 832 128 704
Cusp forms 704 128 576
Eisenstein series 128 0 128

## Trace form

 $$128q - 16q^{4} - 24q^{5} + 20q^{7} - 16q^{9} + O(q^{10})$$ $$128q - 16q^{4} - 24q^{5} + 20q^{7} - 16q^{9} + 8q^{11} + 4q^{14} - 12q^{15} + 16q^{16} + 60q^{17} - 4q^{22} + 8q^{23} - 24q^{26} - 10q^{28} - 40q^{29} + 18q^{31} - 6q^{33} + 40q^{35} - 32q^{36} - 28q^{37} + 24q^{38} + 30q^{40} - 2q^{42} + 12q^{44} - 24q^{45} + 48q^{47} + 72q^{49} + 40q^{51} - 8q^{56} + 10q^{58} + 4q^{60} - 60q^{61} + 20q^{63} + 32q^{64} + 32q^{67} - 60q^{68} - 50q^{70} - 48q^{71} - 180q^{73} - 40q^{74} + 24q^{75} - 80q^{77} - 60q^{79} - 36q^{80} + 16q^{81} - 96q^{82} - 160q^{85} - 36q^{86} - 22q^{88} - 48q^{89} - 124q^{91} + 16q^{92} - 28q^{93} - 20q^{95} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(462, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
462.2.ba.a $$64$$ $$3.689$$ None $$0$$ $$0$$ $$-22$$ $$4$$
462.2.ba.b $$64$$ $$3.689$$ None $$0$$ $$0$$ $$-2$$ $$16$$

## Decomposition of $$S_{2}^{\mathrm{old}}(462, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$