gp: [N,k,chi] = [882,6,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Newform invariants
sage: traces = [2,-8,0,32,53,0,0,-128,0,-212,-191]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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 = 1 2 ( 1 + 9601 ) \beta = \frac{1}{2}(1 + \sqrt{9601}) β = 2 1 ( 1 + 9 6 0 1 ) 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)
p p p
Sign
2 2 2
+ 1 +1 + 1
3 3 3
− 1 -1 − 1
7 7 7
+ 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 6 n e w ( Γ 0 ( 882 ) ) S_{6}^{\mathrm{new}}(\Gamma_0(882)) S 6 n e w ( Γ 0 ( 8 8 2 ) )
T 5 2 − 53 T 5 − 1698 T_{5}^{2} - 53T_{5} - 1698 T 5 2 − 5 3 T 5 − 1 6 9 8
T 11 2 + 191 T 11 − 50886 T_{11}^{2} + 191T_{11} - 50886 T 1 1 2 + 1 9 1 T 1 1 − 5 0 8 8 6
p p p F p ( T ) F_p(T) F p ( T )
2 2 2
( T + 4 ) 2 (T + 4)^{2} ( T + 4 ) 2
3 3 3
T 2 T^{2} T 2
5 5 5
T 2 − 53 T − 1698 T^{2} - 53T - 1698 T 2 − 5 3 T − 1 6 9 8
7 7 7
T 2 T^{2} T 2
11 11 1 1
T 2 + 191 T − 50886 T^{2} + 191T - 50886 T 2 + 1 9 1 T − 5 0 8 8 6
13 13 1 3
T 2 + 379 T − 254520 T^{2} + 379T - 254520 T 2 + 3 7 9 T − 2 5 4 5 2 0
17 17 1 7
T 2 − 340 T − 931200 T^{2} - 340T - 931200 T 2 − 3 4 0 T − 9 3 1 2 0 0
19 19 1 9
T 2 + 1769 T − 2868440 T^{2} + 1769 T - 2868440 T 2 + 1 7 6 9 T − 2 8 6 8 4 4 0
23 23 2 3
T 2 + 3236 T + 2579520 T^{2} + 3236 T + 2579520 T 2 + 3 2 3 6 T + 2 5 7 9 5 2 0
29 29 2 9
T 2 + 4459 T − 3960660 T^{2} + 4459 T - 3960660 T 2 + 4 4 5 9 T − 3 9 6 0 6 6 0
31 31 3 1
T 2 − 1994 T − 63563115 T^{2} - 1994 T - 63563115 T 2 − 1 9 9 4 T − 6 3 5 6 3 1 1 5
37 37 3 7
T 2 − 20587 T + 99713092 T^{2} - 20587 T + 99713092 T 2 − 2 0 5 8 7 T + 9 9 7 1 3 0 9 2
41 41 4 1
T 2 + 8814 T + 8966160 T^{2} + 8814 T + 8966160 T 2 + 8 8 1 4 T + 8 9 6 6 1 6 0
43 43 4 3
T 2 − 15853 T + 44661910 T^{2} - 15853 T + 44661910 T 2 − 1 5 8 5 3 T + 4 4 6 6 1 9 1 0
47 47 4 7
T 2 + 33912 T + 229093452 T^{2} + 33912 T + 229093452 T 2 + 3 3 9 1 2 T + 2 2 9 0 9 3 4 5 2
53 53 5 3
T 2 + 49239 T + 484607124 T^{2} + 49239 T + 484607124 T 2 + 4 9 2 3 9 T + 4 8 4 6 0 7 1 2 4
59 59 5 9
T 2 − 56735 T + 800680236 T^{2} - 56735 T + 800680236 T 2 − 5 6 7 3 5 T + 8 0 0 6 8 0 2 3 6
61 61 6 1
T 2 + ⋯ + 1136874660 T^{2} + \cdots + 1136874660 T 2 + ⋯ + 1 1 3 6 8 7 4 6 6 0
67 67 6 7
T 2 + ⋯ + 1160899190 T^{2} + \cdots + 1160899190 T 2 + ⋯ + 1 1 6 0 8 9 9 1 9 0
71 71 7 1
T 2 + ⋯ − 4289674884 T^{2} + \cdots - 4289674884 T 2 + ⋯ − 4 2 8 9 6 7 4 8 8 4
73 73 7 3
T 2 + ⋯ − 1835129806 T^{2} + \cdots - 1835129806 T 2 + ⋯ − 1 8 3 5 1 2 9 8 0 6
79 79 7 9
T 2 + ⋯ − 2156463813 T^{2} + \cdots - 2156463813 T 2 + ⋯ − 2 1 5 6 4 6 3 8 1 3
83 83 8 3
T 2 + ⋯ − 7511023590 T^{2} + \cdots - 7511023590 T 2 + ⋯ − 7 5 1 1 0 2 3 5 9 0
89 89 8 9
T 2 + ⋯ + 7687683936 T^{2} + \cdots + 7687683936 T 2 + ⋯ + 7 6 8 7 6 8 3 9 3 6
97 97 9 7
T 2 + ⋯ − 5231869258 T^{2} + \cdots - 5231869258 T 2 + ⋯ − 5 2 3 1 8 6 9 2 5 8
show more
show less
