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G = DirichletGroup(25); G
Group of Dirichlet characters of modulus 25 over Cyclotomic Field of order 20 and degree 8 
len(G)
20 
X = G.galois_orbits(); X
[ [Dirichlet character modulo 25 of conductor 1 mapping 2 |--> 1], [Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^3, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^7, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^7 - zeta20^5 + zeta20^3 - zeta20, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^3, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^7, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^7 + zeta20^5 - zeta20^3 + zeta20], [Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^2, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^6, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^4, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^6 + zeta20^4 - zeta20^2 + 1], [Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^4, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> zeta20^6 - zeta20^4 + zeta20^2 - 1, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^2, Dirichlet character modulo 25 of conductor 25 mapping 2 |--> -zeta20^6], [Dirichlet character modulo 25 of conductor 5 mapping 2 |--> zeta20^5, Dirichlet character modulo 25 of conductor 5 mapping 2 |--> -zeta20^5], [Dirichlet character modulo 25 of conductor 5 mapping 2 |--> -1] ] 
for z in X:
    chi = z[0]
    S = CuspForms(chi,4)
    print S
Cuspidal subspace of dimension 5 of Modular Forms space of dimension 11 for Congruence Subgroup Gamma0(25) of weight 4 over Rational Field Cuspidal subspace of dimension 0 of Modular Forms space of dimension 0, character [zeta20] and weight 4 over Cyclotomic Field of order 20 and degree 8 Cuspidal subspace of dimension 6 of Modular Forms space of dimension 8, character [zeta10] and weight 4 over Cyclotomic Field of order 10 and degree 4 Cuspidal subspace of dimension 7 of Modular Forms space of dimension 9, character [zeta5] and weight 4 over Cyclotomic Field of order 5 and degree 4 Cuspidal subspace of dimension 0 of Modular Forms space of dimension 0, character [zeta4] and weight 4 over Cyclotomic Field of order 4 and degree 2 Cuspidal subspace of dimension 4 of Modular Forms space of dimension 10, character [-1] and weight 4 over Rational Field 
chi = X[-1][0]
chi
Dirichlet character modulo 25 of conductor 5 mapping 2 |--> -1 
S = CuspForms(chi, 4); S
Cuspidal subspace of dimension 4 of Modular Forms space of dimension 10, character [-1] and weight 4 over Rational Field 
N = S.newforms('a')
for f in N:
    print f.q_expansion(10)
q + a0*q^2 - 7*a0*q^3 + 7*q^4 + 7*q^6 + 6*a0*q^7 + 15*a0*q^8 - 22*q^9 + O(q^10) q + a1*q^2 + 1/2*a1*q^3 - 8*q^4 - 8*q^6 - 3/2*a1*q^7 + 23*q^9 + O(q^10) 
N[0].parent()
Cuspidal subspace of dimension 4 of Modular Forms space of dimension 10, character [-1] and weight 4 over Number Field in a0 with defining polynomial x^2 + 1 
N[0].parent().base_ring()
Number Field in a0 with defining polynomial x^2 + 1