# Properties

 Label 57.2.f Level 57 Weight 2 Character orbit f Rep. character $$\chi_{57}(8,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 8 Newforms 1 Sturm bound 13 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$57 = 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 57.f (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$57$$ Character field: $$\Q(\zeta_{6})$$ Newforms: $$1$$ Sturm bound: $$13$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(57, [\chi])$$.

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

## Trace form

 $$8q + 4q^{6} - 16q^{7} - 4q^{9} + O(q^{10})$$ $$8q + 4q^{6} - 16q^{7} - 4q^{9} - 12q^{10} + 12q^{13} + 4q^{16} - 12q^{21} + 12q^{22} + 4q^{24} - 12q^{25} + 12q^{28} - 8q^{30} + 24q^{33} + 24q^{34} + 16q^{39} - 12q^{40} - 20q^{42} - 16q^{43} + 32q^{45} + 24q^{48} - 48q^{51} - 24q^{52} - 4q^{54} + 16q^{55} - 28q^{57} - 64q^{58} - 24q^{60} + 28q^{61} + 8q^{63} - 32q^{64} - 4q^{66} + 36q^{70} - 24q^{72} + 12q^{73} + 60q^{76} + 36q^{78} + 24q^{79} + 28q^{81} + 16q^{82} + 32q^{87} + 12q^{90} - 48q^{91} - 4q^{93} + 72q^{96} + 24q^{97} - 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(57, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
57.2.f.a $$8$$ $$0.455$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$-16$$ $$q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots$$