gp: [N,k,chi] = [5,18,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Newform invariants
sage: traces = [2]
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)
Coefficients of the q q q β = 36 39 \beta = 36\sqrt{39} β = 3 6 3 9 q q q trace form .
For each embedding ι m \iota_m ι m ι m ( a n ) \iota_m(a_n) ι m ( a n )
For more information on an embedded modular form you can click on its label.
gp: mfembed(f)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
T 2 2 − 680 T 2 + 65056 T_{2}^{2} - 680T_{2} + 65056 T 2 2 − 6 8 0 T 2 + 6 5 0 5 6 S 18 n e w ( Γ 0 ( 5 ) ) S_{18}^{\mathrm{new}}(\Gamma_0(5)) S 1 8 n e w ( Γ 0 ( 5 ) )
p p p F p ( T ) F_p(T) F p ( T )
2 2 2
T 2 − 680 T + 65056 T^{2} - 680T + 65056 T 2 − 6 8 0 T + 6 5 0 5 6
3 3 3
T 2 + 10980 T − 106530876 T^{2} + 10980 T - 106530876 T 2 + 1 0 9 8 0 T − 1 0 6 5 3 0 8 7 6
5 5 5
( T + 390625 ) 2 (T + 390625)^{2} ( T + 3 9 0 6 2 5 ) 2
7 7 7
T 2 + ⋯ + 15270966784836 T^{2} + \cdots + 15270966784836 T 2 + ⋯ + 1 5 2 7 0 9 6 6 7 8 4 8 3 6
11 11 1 1
T 2 + ⋯ + 23 ⋯ 84 T^{2} + \cdots + 23\!\cdots\!84 T 2 + ⋯ + 2 3 ⋯ 8 4
13 13 1 3
T 2 + ⋯ − 18 ⋯ 16 T^{2} + \cdots - 18\!\cdots\!16 T 2 + ⋯ − 1 8 ⋯ 1 6
17 17 1 7
T 2 + ⋯ + 38 ⋯ 96 T^{2} + \cdots + 38\!\cdots\!96 T 2 + ⋯ + 3 8 ⋯ 9 6
19 19 1 9
T 2 + ⋯ − 64 ⋯ 00 T^{2} + \cdots - 64\!\cdots\!00 T 2 + ⋯ − 6 4 ⋯ 0 0
23 23 2 3
T 2 + ⋯ + 95 ⋯ 44 T^{2} + \cdots + 95\!\cdots\!44 T 2 + ⋯ + 9 5 ⋯ 4 4
29 29 2 9
T 2 + ⋯ + 42 ⋯ 00 T^{2} + \cdots + 42\!\cdots\!00 T 2 + ⋯ + 4 2 ⋯ 0 0
31 31 3 1
T 2 + ⋯ − 44 ⋯ 56 T^{2} + \cdots - 44\!\cdots\!56 T 2 + ⋯ − 4 4 ⋯ 5 6
37 37 3 7
T 2 + ⋯ − 72 ⋯ 84 T^{2} + \cdots - 72\!\cdots\!84 T 2 + ⋯ − 7 2 ⋯ 8 4
41 41 4 1
T 2 + ⋯ + 52 ⋯ 24 T^{2} + \cdots + 52\!\cdots\!24 T 2 + ⋯ + 5 2 ⋯ 2 4
43 43 4 3
T 2 + ⋯ − 19 ⋯ 36 T^{2} + \cdots - 19\!\cdots\!36 T 2 + ⋯ − 1 9 ⋯ 3 6
47 47 4 7
T 2 + ⋯ + 62 ⋯ 76 T^{2} + \cdots + 62\!\cdots\!76 T 2 + ⋯ + 6 2 ⋯ 7 6
53 53 5 3
T 2 + ⋯ + 28 ⋯ 24 T^{2} + \cdots + 28\!\cdots\!24 T 2 + ⋯ + 2 8 ⋯ 2 4
59 59 5 9
T 2 + ⋯ + 19 ⋯ 00 T^{2} + \cdots + 19\!\cdots\!00 T 2 + ⋯ + 1 9 ⋯ 0 0
61 61 6 1
T 2 + ⋯ − 13 ⋯ 16 T^{2} + \cdots - 13\!\cdots\!16 T 2 + ⋯ − 1 3 ⋯ 1 6
67 67 6 7
T 2 + ⋯ − 49 ⋯ 04 T^{2} + \cdots - 49\!\cdots\!04 T 2 + ⋯ − 4 9 ⋯ 0 4
71 71 7 1
T 2 + ⋯ − 75 ⋯ 36 T^{2} + \cdots - 75\!\cdots\!36 T 2 + ⋯ − 7 5 ⋯ 3 6
73 73 7 3
T 2 + ⋯ − 51 ⋯ 56 T^{2} + \cdots - 51\!\cdots\!56 T 2 + ⋯ − 5 1 ⋯ 5 6
79 79 7 9
T 2 + ⋯ − 71 ⋯ 00 T^{2} + \cdots - 71\!\cdots\!00 T 2 + ⋯ − 7 1 ⋯ 0 0
83 83 8 3
T 2 + ⋯ + 63 ⋯ 04 T^{2} + \cdots + 63\!\cdots\!04 T 2 + ⋯ + 6 3 ⋯ 0 4
89 89 8 9
T 2 + ⋯ + 32 ⋯ 00 T^{2} + \cdots + 32\!\cdots\!00 T 2 + ⋯ + 3 2 ⋯ 0 0
97 97 9 7
T 2 + ⋯ + 16 ⋯ 76 T^{2} + \cdots + 16\!\cdots\!76 T 2 + ⋯ + 1 6 ⋯ 7 6
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