# Properties

 Label 462.2.y Level $462$ Weight $2$ Character orbit 462.y Rep. character $\chi_{462}(25,\cdot)$ Character field $\Q(\zeta_{15})$ Dimension $128$ Newform subspaces $4$ Sturm bound $192$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.y (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$2$$ 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

 $$128q + 16q^{4} + 8q^{5} + 8q^{6} + 8q^{7} + 16q^{9} + O(q^{10})$$ $$128q + 16q^{4} + 8q^{5} + 8q^{6} + 8q^{7} + 16q^{9} + 36q^{10} + 8q^{11} + 16q^{13} + 4q^{14} + 12q^{15} + 16q^{16} + 12q^{17} - 16q^{20} - 4q^{22} + 8q^{23} - 4q^{24} + 40q^{25} + 8q^{26} + 22q^{28} + 24q^{29} - 8q^{30} - 6q^{31} + 2q^{33} + 32q^{34} + 8q^{35} - 32q^{36} + 20q^{37} + 8q^{38} - 14q^{40} - 24q^{41} + 14q^{42} - 16q^{43} - 12q^{44} + 8q^{45} + 88q^{47} + 8q^{49} - 24q^{51} - 8q^{52} + 16q^{53} + 16q^{54} + 12q^{55} + 8q^{56} + 16q^{57} - 2q^{58} - 32q^{59} + 4q^{60} + 20q^{61} - 96q^{62} + 20q^{63} - 32q^{64} - 96q^{65} - 96q^{67} + 12q^{68} - 40q^{69} - 66q^{70} - 144q^{71} - 32q^{73} - 16q^{74} + 8q^{75} - 80q^{76} - 64q^{77} - 16q^{79} - 12q^{80} + 16q^{81} - 24q^{82} - 208q^{83} - 96q^{85} - 36q^{86} + 4q^{87} - 18q^{88} - 80q^{89} + 8q^{90} - 36q^{91} - 16q^{92} + 28q^{93} - 56q^{94} - 12q^{95} - 4q^{96} - 24q^{97} - 48q^{98} - 16q^{99} + O(q^{100})$$

## 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.y.a $$24$$ $$3.689$$ None $$-3$$ $$-3$$ $$5$$ $$11$$
462.2.y.b $$24$$ $$3.689$$ None $$3$$ $$3$$ $$5$$ $$-5$$
462.2.y.c $$40$$ $$3.689$$ None $$-5$$ $$5$$ $$1$$ $$9$$
462.2.y.d $$40$$ $$3.689$$ None $$5$$ $$-5$$ $$-3$$ $$-7$$

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

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