gp: [N,k,chi] = [175,7,Mod(76,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.76");
S:= CuspForms(chi, 7);
N := Newforms(S);
Newform invariants
sage: traces = [1,-9]
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
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 / 175 Z ) × \left(\mathbb{Z}/175\mathbb{Z}\right)^\times ( Z / 1 7 5 Z ) × .
n n n
101 101 1 0 1
127 127 1 2 7
χ ( n ) \chi(n) χ ( n )
− 1 -1 − 1
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 + 9 T_{2} + 9 T 2 + 9
T2 + 9
acting on S 7 n e w ( 175 , [ χ ] ) S_{7}^{\mathrm{new}}(175, [\chi]) S 7 n e w ( 1 7 5 , [ χ ] ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
T + 9 T + 9 T + 9
T + 9
3 3 3
T T T
T
5 5 5
T T T
T
7 7 7
T − 343 T - 343 T − 3 4 3
T - 343
11 11 1 1
T − 1962 T - 1962 T − 1 9 6 2
T - 1962
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 − 22734 T - 22734 T − 2 2 7 3 4
T - 22734
29 29 2 9
T + 21222 T + 21222 T + 2 1 2 2 2
T + 21222
31 31 3 1
T T T
T
37 37 3 7
T + 101194 T + 101194 T + 1 0 1 1 9 4
T + 101194
41 41 4 1
T T T
T
43 43 4 3
T − 126614 T - 126614 T − 1 2 6 6 1 4
T - 126614
47 47 4 7
T T T
T
53 53 5 3
T + 50346 T + 50346 T + 5 0 3 4 6
T + 50346
59 59 5 9
T T T
T
61 61 6 1
T T T
T
67 67 6 7
T − 53926 T - 53926 T − 5 3 9 2 6
T - 53926
71 71 7 1
T + 242478 T + 242478 T + 2 4 2 4 7 8
T + 242478
73 73 7 3
T T T
T
79 79 7 9
T − 929378 T - 929378 T − 9 2 9 3 7 8
T - 929378
83 83 8 3
T T T
T
89 89 8 9
T T T
T
97 97 9 7
T T T
T
show more
show less