Level N=20=22×5

k=2, chi=[1,1]
dim S2(20,chi) = 1

Hecke
pcharpoly(Tp)
2x
3x +2
5x +1

Eigenforms
f1= q-2*q^3-q^5+2*q^7+q^9+2*q^13

L(f,1)=/=0.

k=2, chi=[2,4]
dim S2(20,chi) = 1
a^2+1=0

Hecke
pcharpoly(Tp)
2x+(a+1)
3x
5x+(-a+2)
7x

Eigenforms
f1= q+(-a-1)q^2+2aq^4+(a-2)q^5+(-2a+2)q^8



k=3, chi=[1,4]
dim S3(20,chi) = 3
a^2+1=0

Hecke
pcharpoly(T_p)
2x^2(x+(a+1))
3x^3+(-3*a+3)*x^2+(8*a+8)
5x^3+(6*a+3)*x^2+(30*a+15)*x+100*a-75

Eigenforms
f1= q+(-a-1)*q^2+2*a*q^4+(a-2)*q^5+(-2*a+2)*q^8
f2= q+(-a-1)*q^2+2*a*q^4+(a-2)*q^5+(-2*a+2)*q^8
f3= q+(-a-1)*q^2+2*a*q^4+(a-2)*q^5+(-2*a+2)*q^8