gp: [N,k,chi] = [11,33,Mod(10,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.10");
S:= CuspForms(chi, 33);
N := Newforms(S);
Newform invariants
sage: traces = [1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == 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)
Character values
We give the values of χ \chi χ on generators for ( Z / 11 Z ) × \left(\mathbb{Z}/11\mathbb{Z}\right)^\times ( Z / 1 1 Z ) × .
n n n
2 2 2
χ ( n ) \chi(n) χ ( n )
− 1 -1 − 1
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
This newform subspace can be constructed as the kernel of the linear operator
T 2 T_{2} T 2
T2
acting on S 33 n e w ( 11 , [ χ ] ) S_{33}^{\mathrm{new}}(11, [\chi]) S 3 3 n e w ( 1 1 , [ χ ] ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T T T
T
3 3 3
T + 85968833 T + 85968833 T + 8 5 9 6 8 8 3 3
T + 85968833
5 5 5
T + 9728091649 T + 9728091649 T + 9 7 2 8 0 9 1 6 4 9
T + 9728091649
7 7 7
T T T
T
11 11 1 1
T − 45 ⋯ 61 T - 45\!\cdots\!61 T − 4 5 ⋯ 6 1
T - 45949729863572161
13 13 1 3
T T T
T
17 17 1 7
T T T
T
19 19 1 9
T T T
T
23 23 2 3
T − 36 ⋯ 47 T - 36\!\cdots\!47 T − 3 6 ⋯ 4 7
T - 3656631949033345760447
29 29 2 9
T T T
T
31 31 3 1
T + 10 ⋯ 13 T + 10\!\cdots\!13 T + 1 0 ⋯ 1 3
T + 1006459202425404995301313
37 37 3 7
T − 17 ⋯ 07 T - 17\!\cdots\!07 T − 1 7 ⋯ 0 7
T - 17726726040327497823316607
41 41 4 1
T T T
T
43 43 4 3
T T T
T
47 47 4 7
T + 10 ⋯ 58 T + 10\!\cdots\!58 T + 1 0 ⋯ 5 8
T + 1020566006447389822959797758
53 53 5 3
T − 40 ⋯ 42 T - 40\!\cdots\!42 T − 4 0 ⋯ 4 2
T - 4022797084351571925113466242
59 59 5 9
T − 33 ⋯ 07 T - 33\!\cdots\!07 T − 3 3 ⋯ 0 7
T - 33520999946136001669135487807
61 61 6 1
T T T
T
67 67 6 7
T + 15 ⋯ 13 T + 15\!\cdots\!13 T + 1 5 ⋯ 1 3
T + 153526925358039096047591099713
71 71 7 1
T − 70 ⋯ 67 T - 70\!\cdots\!67 T − 7 0 ⋯ 6 7
T - 708325301570462956915970875967
73 73 7 3
T T T
T
79 79 7 9
T T T
T
83 83 8 3
T T T
T
89 89 8 9
T + 30 ⋯ 53 T + 30\!\cdots\!53 T + 3 0 ⋯ 5 3
T + 30353141869613419294864684580353
97 97 9 7
T + 40 ⋯ 33 T + 40\!\cdots\!33 T + 4 0 ⋯ 3 3
T + 40247763790655769287984856095233
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