gp: [N,k,chi] = [46,8,Mod(1,46)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(46, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("46.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Newform invariants
sage: traces = [3,24]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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
23 23 2 3
+ 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 3 + 12 T 3 2 − 1329 T 3 − 23400 T_{3}^{3} + 12T_{3}^{2} - 1329T_{3} - 23400 T 3 3 + 1 2 T 3 2 − 1 3 2 9 T 3 − 2 3 4 0 0
T3^3 + 12*T3^2 - 1329*T3 - 23400
acting on S 8 n e w ( Γ 0 ( 46 ) ) S_{8}^{\mathrm{new}}(\Gamma_0(46)) S 8 n e w ( Γ 0 ( 4 6 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
( T − 8 ) 3 (T - 8)^{3} ( T − 8 ) 3
(T - 8)^3
3 3 3
T 3 + 12 T 2 + ⋯ − 23400 T^{3} + 12 T^{2} + \cdots - 23400 T 3 + 1 2 T 2 + ⋯ − 2 3 4 0 0
T^3 + 12*T^2 - 1329*T - 23400
5 5 5
T 3 + 570 T 2 + ⋯ − 13183600 T^{3} + 570 T^{2} + \cdots - 13183600 T 3 + 5 7 0 T 2 + ⋯ − 1 3 1 8 3 6 0 0
T^3 + 570*T^2 + 35460*T - 13183600
7 7 7
T 3 + ⋯ − 2391036528 T^{3} + \cdots - 2391036528 T 3 + ⋯ − 2 3 9 1 0 3 6 5 2 8
T^3 + 1382*T^2 - 1916324*T - 2391036528
11 11 1 1
T 3 + ⋯ − 77567772648 T^{3} + \cdots - 77567772648 T 3 + ⋯ − 7 7 5 6 7 7 7 2 6 4 8
T^3 + 11792*T^2 + 21863536*T - 77567772648
13 13 1 3
T 3 + ⋯ − 164166584566 T^{3} + \cdots - 164166584566 T 3 + ⋯ − 1 6 4 1 6 6 5 8 4 5 6 6
T^3 + 12*T^2 - 135635355*T - 164166584566
17 17 1 7
T 3 + ⋯ − 14898856912840 T^{3} + \cdots - 14898856912840 T 3 + ⋯ − 1 4 8 9 8 8 5 6 9 1 2 8 4 0
T^3 + 25584*T^2 - 737189160*T - 14898856912840
19 19 1 9
T 3 + ⋯ − 556058270392 T^{3} + \cdots - 556058270392 T 3 + ⋯ − 5 5 6 0 5 8 2 7 0 3 9 2
T^3 + 42966*T^2 - 520654260*T - 556058270392
23 23 2 3
( T + 12167 ) 3 (T + 12167)^{3} ( T + 1 2 1 6 7 ) 3
(T + 12167)^3
29 29 2 9
T 3 + ⋯ − 33 ⋯ 02 T^{3} + \cdots - 33\!\cdots\!02 T 3 + ⋯ − 3 3 ⋯ 0 2
T^3 + 11196*T^2 - 41062703763*T - 3360105339204602
31 31 3 1
T 3 + ⋯ − 829548394660080 T^{3} + \cdots - 829548394660080 T 3 + ⋯ − 8 2 9 5 4 8 3 9 4 6 6 0 0 8 0
T^3 - 33724*T^2 - 52975924281*T - 829548394660080
37 37 3 7
T 3 + ⋯ − 18 ⋯ 12 T^{3} + \cdots - 18\!\cdots\!12 T 3 + ⋯ − 1 8 ⋯ 1 2
T^3 - 90570*T^2 - 181834402428*T - 18789527807005712
41 41 4 1
T 3 + ⋯ − 19 ⋯ 74 T^{3} + \cdots - 19\!\cdots\!74 T 3 + ⋯ − 1 9 ⋯ 7 4
T^3 + 452488*T^2 + 32885169945*T - 1910868432975774
43 43 4 3
T 3 + ⋯ − 14 ⋯ 60 T^{3} + \cdots - 14\!\cdots\!60 T 3 + ⋯ − 1 4 ⋯ 6 0
T^3 - 8074*T^2 - 522699845536*T - 142047576967938560
47 47 4 7
T 3 + ⋯ + 23 ⋯ 00 T^{3} + \cdots + 23\!\cdots\!00 T 3 + ⋯ + 2 3 ⋯ 0 0
T^3 - 160540*T^2 - 449199138465*T + 23278082563317600
53 53 5 3
T 3 + ⋯ + 11 ⋯ 72 T^{3} + \cdots + 11\!\cdots\!72 T 3 + ⋯ + 1 1 ⋯ 7 2
T^3 - 1288796*T^2 - 1273445430100*T + 1197012982392938672
59 59 5 9
T 3 + ⋯ + 19 ⋯ 72 T^{3} + \cdots + 19\!\cdots\!72 T 3 + ⋯ + 1 9 ⋯ 7 2
T^3 - 742720*T^2 - 5242214144928*T + 1913489662690539072
61 61 6 1
T 3 + ⋯ − 23 ⋯ 88 T^{3} + \cdots - 23\!\cdots\!88 T 3 + ⋯ − 2 3 ⋯ 8 8
T^3 - 4089196*T^2 + 5445726539732*T - 2342757220533670688
67 67 6 7
T 3 + ⋯ + 84 ⋯ 80 T^{3} + \cdots + 84\!\cdots\!80 T 3 + ⋯ + 8 4 ⋯ 8 0
T^3 + 7060728*T^2 + 14060311039056*T + 8484114220543386280
71 71 7 1
T 3 + ⋯ − 54 ⋯ 20 T^{3} + \cdots - 54\!\cdots\!20 T 3 + ⋯ − 5 4 ⋯ 2 0
T^3 + 5044032*T^2 - 10824246758349*T - 54370544658809955120
73 73 7 3
T 3 + ⋯ + 16 ⋯ 82 T^{3} + \cdots + 16\!\cdots\!82 T 3 + ⋯ + 1 6 ⋯ 8 2
T^3 + 8838444*T^2 + 21928258571265*T + 16179099200995994082
79 79 7 9
T 3 + ⋯ − 43 ⋯ 12 T^{3} + \cdots - 43\!\cdots\!12 T 3 + ⋯ − 4 3 ⋯ 1 2
T^3 + 3851056*T^2 - 12590404166460*T - 43573945220521109712
83 83 8 3
T 3 + ⋯ − 77 ⋯ 88 T^{3} + \cdots - 77\!\cdots\!88 T 3 + ⋯ − 7 7 ⋯ 8 8
T^3 + 8398012*T^2 - 13700768731504*T - 77394116099901860488
89 89 8 9
T 3 + ⋯ + 49 ⋯ 96 T^{3} + \cdots + 49\!\cdots\!96 T 3 + ⋯ + 4 9 ⋯ 9 6
T^3 + 1319178*T^2 - 49442954126040*T + 49254913986675715296
97 97 9 7
T 3 + ⋯ + 59 ⋯ 72 T^{3} + \cdots + 59\!\cdots\!72 T 3 + ⋯ + 5 9 ⋯ 7 2
T^3 + 1020584*T^2 - 204733935064608*T + 590214238851739953672
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