gp: [N,k,chi] = [200,4,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
sage: traces = [1,0,1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
gp: f = lf[1] \\ Warning: the index may be different
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
For each embedding ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι m ( a n ) are shown below.
For more information on an embedded modular form you can click on its label.
gp: mfembed(f)
Refresh table
p p p
Sign
2 2 2
+ 1 +1 + 1
5 5 5
− 1 -1 − 1
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
T 3 − 1 T_{3} - 1 T 3 − 1
T3 - 1
acting on S 4 n e w ( Γ 0 ( 200 ) ) S_{4}^{\mathrm{new}}(\Gamma_0(200)) S 4 n e w ( Γ 0 ( 2 0 0 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T T T
T
3 3 3
T − 1 T - 1 T − 1
T - 1
5 5 5
T T T
T
7 7 7
T + 6 T + 6 T + 6
T + 6
11 11 1 1
T + 19 T + 19 T + 1 9
T + 19
13 13 1 3
T − 12 T - 12 T − 1 2
T - 12
17 17 1 7
T + 75 T + 75 T + 7 5
T + 75
19 19 1 9
T + 91 T + 91 T + 9 1
T + 91
23 23 2 3
T − 174 T - 174 T − 1 7 4
T - 174
29 29 2 9
T + 272 T + 272 T + 2 7 2
T + 272
31 31 3 1
T + 230 T + 230 T + 2 3 0
T + 230
37 37 3 7
T + 182 T + 182 T + 1 8 2
T + 182
41 41 4 1
T − 117 T - 117 T − 1 1 7
T - 117
43 43 4 3
T − 372 T - 372 T − 3 7 2
T - 372
47 47 4 7
T + 52 T + 52 T + 5 2
T + 52
53 53 5 3
T + 402 T + 402 T + 4 0 2
T + 402
59 59 5 9
T − 312 T - 312 T − 3 1 2
T - 312
61 61 6 1
T − 170 T - 170 T − 1 7 0
T - 170
67 67 6 7
T − 763 T - 763 T − 7 6 3
T - 763
71 71 7 1
T + 52 T + 52 T + 5 2
T + 52
73 73 7 3
T + 981 T + 981 T + 9 8 1
T + 981
79 79 7 9
T − 1054 T - 1054 T − 1 0 5 4
T - 1054
83 83 8 3
T − 351 T - 351 T − 3 5 1
T - 351
89 89 8 9
T − 799 T - 799 T − 7 9 9
T - 799
97 97 9 7
T − 962 T - 962 T − 9 6 2
T - 962
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