# Properties

 Label 61.2.f Level 61 Weight 2 Character orbit f Rep. character $$\chi_{61}(14,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 10 Newform subspaces 2 Sturm bound 10 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$61$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 61.f (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$61$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(61, [\chi])$$.

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

## Trace form

 $$10q - 3q^{2} - 6q^{3} + 9q^{4} + 3q^{5} - 15q^{6} - 9q^{7} + 4q^{9} + O(q^{10})$$ $$10q - 3q^{2} - 6q^{3} + 9q^{4} + 3q^{5} - 15q^{6} - 9q^{7} + 4q^{9} + 3q^{10} - q^{12} - q^{13} - 15q^{16} - 6q^{17} + 9q^{18} + 5q^{19} + 24q^{20} + 18q^{21} - q^{22} - 8q^{25} - 21q^{26} - 6q^{27} - 3q^{29} - 60q^{30} - 21q^{31} + 39q^{32} + 32q^{34} + 21q^{35} + 36q^{36} + 14q^{39} + 12q^{40} - 18q^{41} + 15q^{42} + 6q^{43} - 12q^{44} + 6q^{45} - 17q^{46} - 32q^{48} - 8q^{49} + 12q^{51} - 8q^{52} - 30q^{54} + 12q^{55} - 4q^{57} + 28q^{58} - 9q^{59} - 9q^{61} + 102q^{62} - 42q^{63} - 100q^{64} + 30q^{65} + 22q^{66} - 21q^{67} - 69q^{68} - 72q^{70} - 3q^{71} - 9q^{73} + 3q^{74} + 21q^{75} + 19q^{76} - 9q^{77} + 45q^{78} + 24q^{79} + 57q^{80} - 14q^{81} + 51q^{82} - 48q^{83} - 48q^{86} + 21q^{87} + 96q^{88} + 72q^{90} - 12q^{91} - 69q^{92} - 12q^{93} + 42q^{95} + 120q^{96} + 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(61, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
61.2.f.a $$2$$ $$0.487$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$-4$$ $$-3$$ $$-6$$ $$q+(-1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$$
61.2.f.b $$8$$ $$0.487$$ 8.0.542936601.2 None $$0$$ $$-2$$ $$6$$ $$-3$$ $$q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$$