gp: [N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
Level :
N N N
= = =
7800 = 2 3 ⋅ 3 ⋅ 5 2 ⋅ 13 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 7 8 0 0 = 2 3 ⋅ 3 ⋅ 5 2 ⋅ 1 3
Weight :
k k k
= = =
2 2 2
Character orbit :
[ χ ] [\chi] [ χ ]
= = =
7800.a (trivial)
Newform invariants
sage: traces = [3,0,-3,0,0,0,-1,0,3,0,-3,0,3,0,0,0,3]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == 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
2 2 2
+ 1 +1 + 1
3 3 3
+ 1 +1 + 1
5 5 5
− 1 -1 − 1
13 13 1 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 2 n e w ( Γ 0 ( 7800 ) ) S_{2}^{\mathrm{new}}(\Gamma_0(7800)) S 2 n e w ( Γ 0 ( 7 8 0 0 ) ) :
T 7 3 + T 7 2 − 7 T 7 + 3 T_{7}^{3} + T_{7}^{2} - 7T_{7} + 3 T 7 3 + T 7 2 − 7 T 7 + 3
T7^3 + T7^2 - 7*T7 + 3
T 11 3 + 3 T 11 2 − 17 T 11 − 53 T_{11}^{3} + 3T_{11}^{2} - 17T_{11} - 53 T 1 1 3 + 3 T 1 1 2 − 1 7 T 1 1 − 5 3
T11^3 + 3*T11^2 - 17*T11 - 53
T 17 − 1 T_{17} - 1 T 1 7 − 1
T17 - 1
T 19 3 + 6 T 19 2 − 20 T 19 − 100 T_{19}^{3} + 6T_{19}^{2} - 20T_{19} - 100 T 1 9 3 + 6 T 1 9 2 − 2 0 T 1 9 − 1 0 0
T19^3 + 6*T19^2 - 20*T19 - 100
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T 3 T^{3} T 3
T^3
3 3 3
( T + 1 ) 3 (T + 1)^{3} ( T + 1 ) 3
(T + 1)^3
5 5 5
T 3 T^{3} T 3
T^3
7 7 7
T 3 + T 2 − 7 T + 3 T^{3} + T^{2} - 7T + 3 T 3 + T 2 − 7 T + 3
T^3 + T^2 - 7*T + 3
11 11 1 1
T 3 + 3 T 2 + ⋯ − 53 T^{3} + 3 T^{2} + \cdots - 53 T 3 + 3 T 2 + ⋯ − 5 3
T^3 + 3*T^2 - 17*T - 53
13 13 1 3
( T − 1 ) 3 (T - 1)^{3} ( T − 1 ) 3
(T - 1)^3
17 17 1 7
( T − 1 ) 3 (T - 1)^{3} ( T − 1 ) 3
(T - 1)^3
19 19 1 9
T 3 + 6 T 2 + ⋯ − 100 T^{3} + 6 T^{2} + \cdots - 100 T 3 + 6 T 2 + ⋯ − 1 0 0
T^3 + 6*T^2 - 20*T - 100
23 23 2 3
T 3 − 32 T − 44 T^{3} - 32T - 44 T 3 − 3 2 T − 4 4
T^3 - 32*T - 44
29 29 2 9
T 3 + T 2 + ⋯ − 93 T^{3} + T^{2} + \cdots - 93 T 3 + T 2 + ⋯ − 9 3
T^3 + T^2 - 53*T - 93
31 31 3 1
T 3 + 7 T 2 + ⋯ − 425 T^{3} + 7 T^{2} + \cdots - 425 T 3 + 7 T 2 + ⋯ − 4 2 5
T^3 + 7*T^2 - 65*T - 425
37 37 3 7
T 3 − 14 T 2 + ⋯ − 60 T^{3} - 14 T^{2} + \cdots - 60 T 3 − 1 4 T 2 + ⋯ − 6 0
T^3 - 14*T^2 + 56*T - 60
41 41 4 1
T 3 − 84 T − 52 T^{3} - 84T - 52 T 3 − 8 4 T − 5 2
T^3 - 84*T - 52
43 43 4 3
T 3 + 4 T 2 + ⋯ − 12 T^{3} + 4 T^{2} + \cdots - 12 T 3 + 4 T 2 + ⋯ − 1 2
T^3 + 4*T^2 - 4*T - 12
47 47 4 7
T 3 + T 2 + ⋯ − 89 T^{3} + T^{2} + \cdots - 89 T 3 + T 2 + ⋯ − 8 9
T^3 + T^2 - 83*T - 89
53 53 5 3
T 3 − 5 T 2 + ⋯ + 781 T^{3} - 5 T^{2} + \cdots + 781 T 3 − 5 T 2 + ⋯ + 7 8 1
T^3 - 5*T^2 - 125*T + 781
59 59 5 9
T 3 + 7 T 2 + ⋯ + 9 T^{3} + 7 T^{2} + \cdots + 9 T 3 + 7 T 2 + ⋯ + 9
T^3 + 7*T^2 - 35*T + 9
61 61 6 1
T 3 + 5 T 2 + ⋯ − 9 T^{3} + 5 T^{2} + \cdots - 9 T 3 + 5 T 2 + ⋯ − 9
T^3 + 5*T^2 - 45*T - 9
67 67 6 7
T 3 − 3 T 2 + ⋯ − 15 T^{3} - 3 T^{2} + \cdots - 15 T 3 − 3 T 2 + ⋯ − 1 5
T^3 - 3*T^2 - 17*T - 15
71 71 7 1
T 3 + 10 T 2 + ⋯ − 180 T^{3} + 10 T^{2} + \cdots - 180 T 3 + 1 0 T 2 + ⋯ − 1 8 0
T^3 + 10*T^2 - 12*T - 180
73 73 7 3
T 3 + 10 T 2 + ⋯ + 52 T^{3} + 10 T^{2} + \cdots + 52 T 3 + 1 0 T 2 + ⋯ + 5 2
T^3 + 10*T^2 - 60*T + 52
79 79 7 9
T 3 + 16 T 2 + ⋯ + 100 T^{3} + 16 T^{2} + \cdots + 100 T 3 + 1 6 T 2 + ⋯ + 1 0 0
T^3 + 16*T^2 + 76*T + 100
83 83 8 3
T 3 − 11 T 2 + ⋯ + 255 T^{3} - 11 T^{2} + \cdots + 255 T 3 − 1 1 T 2 + ⋯ + 2 5 5
T^3 - 11*T^2 - 11*T + 255
89 89 8 9
T 3 + 8 T 2 + ⋯ − 48 T^{3} + 8 T^{2} + \cdots - 48 T 3 + 8 T 2 + ⋯ − 4 8
T^3 + 8*T^2 - 32*T - 48
97 97 9 7
T 3 − 26 T 2 + ⋯ − 440 T^{3} - 26 T^{2} + \cdots - 440 T 3 − 2 6 T 2 + ⋯ − 4 4 0
T^3 - 26*T^2 + 196*T - 440
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