gp: [N,k,chi] = [4851,2,Mod(1,4851)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4851, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4851.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: traces = [3,0,0,0,6,0,0,-3,0,-3,-3,0,-3,0,0,-6,-3,0,-9,6,0,0,0]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
gp: f = lf[1] \\ Warning: the index may be different
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
3 3 3
− 1 -1 − 1
7 7 7
− 1 -1 − 1
11 11 1 1
+ 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 2 n e w ( Γ 0 ( 4851 ) ) S_{2}^{\mathrm{new}}(\Gamma_0(4851)) S 2 n e w ( Γ 0 ( 4 8 5 1 ) ) :
T 2 3 − 3 T 2 + 1 T_{2}^{3} - 3T_{2} + 1 T 2 3 − 3 T 2 + 1
T2^3 - 3*T2 + 1
T 5 3 − 6 T 5 2 + 9 T 5 − 1 T_{5}^{3} - 6T_{5}^{2} + 9T_{5} - 1 T 5 3 − 6 T 5 2 + 9 T 5 − 1
T5^3 - 6*T5^2 + 9*T5 - 1
T 13 3 + 3 T 13 2 − 6 T 13 + 1 T_{13}^{3} + 3T_{13}^{2} - 6T_{13} + 1 T 1 3 3 + 3 T 1 3 2 − 6 T 1 3 + 1
T13^3 + 3*T13^2 - 6*T13 + 1
T 17 3 + 3 T 17 2 − 36 T 17 − 127 T_{17}^{3} + 3T_{17}^{2} - 36T_{17} - 127 T 1 7 3 + 3 T 1 7 2 − 3 6 T 1 7 − 1 2 7
T17^3 + 3*T17^2 - 36*T17 - 127
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 3 − 3 T + 1 T^{3} - 3T + 1 T 3 − 3 T + 1
T^3 - 3*T + 1
3 3 3
T 3 T^{3} T 3
T^3
5 5 5
T 3 − 6 T 2 + ⋯ − 1 T^{3} - 6 T^{2} + \cdots - 1 T 3 − 6 T 2 + ⋯ − 1
T^3 - 6*T^2 + 9*T - 1
7 7 7
T 3 T^{3} T 3
T^3
11 11 1 1
( T + 1 ) 3 (T + 1)^{3} ( T + 1 ) 3
(T + 1)^3
13 13 1 3
T 3 + 3 T 2 + ⋯ + 1 T^{3} + 3 T^{2} + \cdots + 1 T 3 + 3 T 2 + ⋯ + 1
T^3 + 3*T^2 - 6*T + 1
17 17 1 7
T 3 + 3 T 2 + ⋯ − 127 T^{3} + 3 T^{2} + \cdots - 127 T 3 + 3 T 2 + ⋯ − 1 2 7
T^3 + 3*T^2 - 36*T - 127
19 19 1 9
T 3 + 9 T 2 + ⋯ + 9 T^{3} + 9 T^{2} + \cdots + 9 T 3 + 9 T 2 + ⋯ + 9
T^3 + 9*T^2 + 18*T + 9
23 23 2 3
T 3 − 57 T + 107 T^{3} - 57T + 107 T 3 − 5 7 T + 1 0 7
T^3 - 57*T + 107
29 29 2 9
T 3 − 3 T 2 + ⋯ − 51 T^{3} - 3 T^{2} + \cdots - 51 T 3 − 3 T 2 + ⋯ − 5 1
T^3 - 3*T^2 - 36*T - 51
31 31 3 1
T 3 + 9 T 2 + ⋯ + 19 T^{3} + 9 T^{2} + \cdots + 19 T 3 + 9 T 2 + ⋯ + 1 9
T^3 + 9*T^2 + 24*T + 19
37 37 3 7
T 3 − 36 T + 72 T^{3} - 36T + 72 T 3 − 3 6 T + 7 2
T^3 - 36*T + 72
41 41 4 1
T 3 − 9 T 2 + ⋯ − 1 T^{3} - 9 T^{2} + \cdots - 1 T 3 − 9 T 2 + ⋯ − 1
T^3 - 9*T^2 + 6*T - 1
43 43 4 3
T 3 − 9 T + 9 T^{3} - 9T + 9 T 3 − 9 T + 9
T^3 - 9*T + 9
47 47 4 7
T 3 + 3 T 2 + ⋯ − 323 T^{3} + 3 T^{2} + \cdots - 323 T 3 + 3 T 2 + ⋯ − 3 2 3
T^3 + 3*T^2 - 78*T - 323
53 53 5 3
T 3 + 9 T 2 + ⋯ − 459 T^{3} + 9 T^{2} + \cdots - 459 T 3 + 9 T 2 + ⋯ − 4 5 9
T^3 + 9*T^2 - 54*T - 459
59 59 5 9
T 3 − 93 T + 19 T^{3} - 93T + 19 T 3 − 9 3 T + 1 9
T^3 - 93*T + 19
61 61 6 1
T 3 + 12 T 2 + ⋯ + 24 T^{3} + 12 T^{2} + \cdots + 24 T 3 + 1 2 T 2 + ⋯ + 2 4
T^3 + 12*T^2 - 36*T + 24
67 67 6 7
T 3 − 12 T − 8 T^{3} - 12T - 8 T 3 − 1 2 T − 8
T^3 - 12*T - 8
71 71 7 1
T 3 − 9 T 2 + ⋯ + 801 T^{3} - 9 T^{2} + \cdots + 801 T 3 − 9 T 2 + ⋯ + 8 0 1
T^3 - 9*T^2 - 90*T + 801
73 73 7 3
T 3 + 6 T 2 + ⋯ + 1 T^{3} + 6 T^{2} + \cdots + 1 T 3 + 6 T 2 + ⋯ + 1
T^3 + 6*T^2 + 9*T + 1
79 79 7 9
T 3 + 3 T 2 + ⋯ + 37 T^{3} + 3 T^{2} + \cdots + 37 T 3 + 3 T 2 + ⋯ + 3 7
T^3 + 3*T^2 - 114*T + 37
83 83 8 3
T 3 + 15 T 2 + ⋯ − 267 T^{3} + 15 T^{2} + \cdots - 267 T 3 + 1 5 T 2 + ⋯ − 2 6 7
T^3 + 15*T^2 + 18*T - 267
89 89 8 9
T 3 + 15 T 2 + ⋯ + 111 T^{3} + 15 T^{2} + \cdots + 111 T 3 + 1 5 T 2 + ⋯ + 1 1 1
T^3 + 15*T^2 + 72*T + 111
97 97 9 7
T 3 + 45 T 2 + ⋯ + 3329 T^{3} + 45 T^{2} + \cdots + 3329 T 3 + 4 5 T 2 + ⋯ + 3 3 2 9
T^3 + 45*T^2 + 672*T + 3329
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