# Properties

 Label 62.2.c Level 62 Weight 2 Character orbit c Rep. character $$\chi_{62}(5,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 4 Newforms 2 Sturm bound 16 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$62 = 2 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 62.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$31$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$2$$ Sturm bound: $$16$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(62, [\chi])$$.

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

## Trace form

 $$4q - 4q^{3} + 4q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 4q^{9} + O(q^{10})$$ $$4q - 4q^{3} + 4q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 4q^{9} - 4q^{10} - 4q^{12} - 10q^{13} + 2q^{14} + 4q^{16} - 6q^{17} - 8q^{18} + 2q^{20} + 10q^{21} + 6q^{22} - 8q^{23} - 2q^{24} + 8q^{27} + 4q^{28} + 16q^{29} + 12q^{30} - 12q^{33} - 4q^{36} + 6q^{37} - 14q^{38} + 40q^{39} - 4q^{40} + 6q^{41} + 8q^{42} - 4q^{43} - 12q^{45} - 8q^{46} - 40q^{47} - 4q^{48} + 4q^{49} + 8q^{50} - 12q^{51} - 10q^{52} - 6q^{53} + 28q^{54} + 12q^{55} + 2q^{56} - 14q^{57} - 8q^{58} - 8q^{61} + 8q^{62} - 32q^{63} + 4q^{64} + 10q^{65} - 24q^{66} + 16q^{67} - 6q^{68} + 12q^{69} - 12q^{70} + 4q^{71} - 8q^{72} + 6q^{73} - 8q^{74} + 8q^{75} + 12q^{77} + 20q^{78} + 2q^{80} - 10q^{81} + 12q^{82} + 4q^{83} + 10q^{84} - 12q^{85} + 6q^{86} - 12q^{87} + 6q^{88} + 24q^{89} - 40q^{91} - 8q^{92} + 14q^{93} + 8q^{94} + 56q^{95} - 2q^{96} + 32q^{97} - 8q^{98} + 24q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(62, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
62.2.c.a $$2$$ $$0.495$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-1$$ $$3$$ $$1$$ $$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots$$
62.2.c.b $$2$$ $$0.495$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-3$$ $$-1$$ $$3$$ $$q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(62, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(62, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 2}$$