gp: [N,k,chi] = [192,4,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, 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("192.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
sage: traces = [1,0,-3,0,-6]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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
3 3 3
+ 1 +1 + 1
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S 4 n e w ( Γ 0 ( 192 ) ) S_{4}^{\mathrm{new}}(\Gamma_0(192)) S 4 n e w ( Γ 0 ( 1 9 2 ) ) :
T 5 + 6 T_{5} + 6 T 5 + 6
T5 + 6
T 7 − 16 T_{7} - 16 T 7 − 1 6
T7 - 16
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T T T
T
3 3 3
T + 3 T + 3 T + 3
T + 3
5 5 5
T + 6 T + 6 T + 6
T + 6
7 7 7
T − 16 T - 16 T − 1 6
T - 16
11 11 1 1
T − 12 T - 12 T − 1 2
T - 12
13 13 1 3
T + 38 T + 38 T + 3 8
T + 38
17 17 1 7
T + 126 T + 126 T + 1 2 6
T + 126
19 19 1 9
T − 20 T - 20 T − 2 0
T - 20
23 23 2 3
T + 168 T + 168 T + 1 6 8
T + 168
29 29 2 9
T + 30 T + 30 T + 3 0
T + 30
31 31 3 1
T − 88 T - 88 T − 8 8
T - 88
37 37 3 7
T + 254 T + 254 T + 2 5 4
T + 254
41 41 4 1
T − 42 T - 42 T − 4 2
T - 42
43 43 4 3
T + 52 T + 52 T + 5 2
T + 52
47 47 4 7
T − 96 T - 96 T − 9 6
T - 96
53 53 5 3
T + 198 T + 198 T + 1 9 8
T + 198
59 59 5 9
T + 660 T + 660 T + 6 6 0
T + 660
61 61 6 1
T − 538 T - 538 T − 5 3 8
T - 538
67 67 6 7
T − 884 T - 884 T − 8 8 4
T - 884
71 71 7 1
T + 792 T + 792 T + 7 9 2
T + 792
73 73 7 3
T − 218 T - 218 T − 2 1 8
T - 218
79 79 7 9
T − 520 T - 520 T − 5 2 0
T - 520
83 83 8 3
T + 492 T + 492 T + 4 9 2
T + 492
89 89 8 9
T − 810 T - 810 T − 8 1 0
T - 810
97 97 9 7
T − 1154 T - 1154 T − 1 1 5 4
T - 1154
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