# Properties

 Label 201.2.d Level 201 Weight 2 Character orbit d Rep. character $$\chi_{201}(200,\cdot)$$ Character field $$\Q$$ Dimension 20 Newforms 1 Sturm bound 45 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$201 = 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 201.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q$$ Newforms: $$1$$ Sturm bound: $$45$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

## Trace form

 $$20q + 12q^{4} - 4q^{6} - 14q^{9} + O(q^{10})$$ $$20q + 12q^{4} - 4q^{6} - 14q^{9} - 12q^{10} + 2q^{15} + 12q^{16} + 24q^{19} + 12q^{21} - 28q^{22} + 2q^{24} - 4q^{25} + 10q^{33} - 44q^{36} + 24q^{37} - 8q^{39} - 32q^{40} - 48q^{49} - 26q^{54} - 8q^{55} - 38q^{60} - 16q^{64} + 32q^{67} + 4q^{73} + 116q^{76} - 30q^{81} - 32q^{82} + 90q^{84} - 40q^{88} + 74q^{90} + 20q^{91} - 2q^{93} + 30q^{96} + O(q^{100})$$

## 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.d.a $$20$$ $$1.605$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+\beta _{5}q^{3}+(1+\beta _{16})q^{4}-\beta _{11}q^{5}+\cdots$$