# Properties

 Label 201.2.f Level 201 Weight 2 Character orbit f Rep. character $$\chi_{201}(38,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 42 Newforms 2 Sturm bound 45 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$201 = 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 201.f (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q(\zeta_{6})$$ Newforms: $$2$$ Sturm bound: $$45$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(201, [\chi])$$.

Total New Old
Modular forms 50 50 0
Cusp forms 42 42 0
Eisenstein series 8 8 0

## Trace form

 $$42q - 22q^{4} - 2q^{6} + 2q^{9} + O(q^{10})$$ $$42q - 22q^{4} - 2q^{6} + 2q^{9} - 6q^{10} + 15q^{12} - 3q^{13} - 26q^{15} - 40q^{16} + 6q^{18} + 2q^{19} + 12q^{21} + 52q^{22} - 26q^{24} + 30q^{25} - 60q^{28} + 57q^{30} - 51q^{31} + 8q^{33} - 12q^{34} - 4q^{36} + 2q^{37} + 14q^{39} - 40q^{40} + 30q^{46} - 66q^{48} - q^{49} - 12q^{51} + 20q^{54} - 16q^{55} - 24q^{57} + 80q^{60} + 15q^{61} + 6q^{63} + 120q^{64} - q^{67} - 21q^{69} + q^{73} + 84q^{76} - 42q^{78} - 9q^{79} - 6q^{81} + 104q^{82} + 27q^{84} - 78q^{85} - 21q^{87} - 62q^{88} - 110q^{90} - 20q^{91} + 2q^{93} - 9q^{96} - 99q^{97} + 87q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(201, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
201.2.f.a $$2$$ $$1.605$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$6$$ $$q+(1-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(4-2\zeta_{6})q^{7}+\cdots$$
201.2.f.b $$40$$ $$1.605$$ None $$0$$ $$0$$ $$0$$ $$-6$$