# Properties

 Label 462.2.j Level $462$ Weight $2$ Character orbit 462.j Rep. character $\chi_{462}(169,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $48$ Newform subspaces $8$ Sturm bound $192$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.j (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$8$$ Sturm bound: $$192$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 416 48 368
Cusp forms 352 48 304
Eisenstein series 64 0 64

## Trace form

 $$48q - 12q^{4} - 12q^{9} + O(q^{10})$$ $$48q - 12q^{4} - 12q^{9} + 32q^{11} + 8q^{13} - 16q^{15} - 12q^{16} - 16q^{17} - 16q^{19} + 16q^{21} - 4q^{22} + 16q^{23} + 24q^{25} - 8q^{26} - 16q^{30} - 16q^{31} - 16q^{33} - 16q^{34} - 12q^{36} + 16q^{37} - 8q^{38} - 16q^{39} - 16q^{41} + 80q^{43} - 8q^{44} - 16q^{47} - 12q^{49} + 48q^{50} - 24q^{51} + 8q^{52} + 56q^{53} + 40q^{55} + 32q^{57} - 24q^{58} + 56q^{59} + 24q^{60} - 24q^{61} + 48q^{62} - 12q^{64} - 80q^{65} + 24q^{66} - 96q^{67} - 16q^{68} + 24q^{69} - 8q^{70} + 8q^{71} - 40q^{73} - 32q^{75} - 16q^{76} - 16q^{77} + 8q^{79} - 12q^{81} - 48q^{82} - 64q^{83} - 4q^{84} - 12q^{85} - 40q^{86} - 32q^{87} - 4q^{88} - 24q^{92} - 4q^{93} - 48q^{94} - 32q^{95} - 16q^{97} - 8q^{99} + O(q^{100})$$

## 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.j.a $$4$$ $$3.689$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$-1$$ $$3$$ $$1$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
462.2.j.b $$4$$ $$3.689$$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$-1$$ $$-1$$ $$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$$
462.2.j.c $$4$$ $$3.689$$ $$\Q(\zeta_{10})$$ None $$1$$ $$-1$$ $$5$$ $$1$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$$
462.2.j.d $$4$$ $$3.689$$ $$\Q(\zeta_{10})$$ None $$1$$ $$1$$ $$-3$$ $$-1$$ $$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$$
462.2.j.e $$8$$ $$3.689$$ 8.0.484000000.9 None $$-2$$ $$-2$$ $$4$$ $$-2$$ $$q+\beta _{2}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots$$
462.2.j.f $$8$$ $$3.689$$ 8.0.64000000.1 None $$-2$$ $$2$$ $$-6$$ $$2$$ $$q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots$$
462.2.j.g $$8$$ $$3.689$$ 8.0.324000000.3 None $$2$$ $$-2$$ $$0$$ $$-2$$ $$q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots$$
462.2.j.h $$8$$ $$3.689$$ 8.0.$$\cdots$$.8 None $$2$$ $$2$$ $$-2$$ $$2$$ $$q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(462, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(22, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(154, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 2}$$