Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 950.f (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficients of the -expansion are expressed in terms of a primitive root of unity . We also show the integral -expansion of the trace form.
Character values
We give the values of on generators for .
Embeddings
For each embedding of the coefficient field, the values are shown below.
For more information on an embedded modular form you can click on its label.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label | ||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
493.1 |
|
−0.707107 | − | 0.707107i | 0 | 1.00000i | 0 | 0 | 1.00000 | − | 1.00000i | 0.707107 | − | 0.707107i | 3.00000i | 0 | ||||||||||||||||||||||||
493.2 | 0.707107 | + | 0.707107i | 0 | 1.00000i | 0 | 0 | 1.00000 | − | 1.00000i | −0.707107 | + | 0.707107i | 3.00000i | 0 | |||||||||||||||||||||||||
607.1 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | 0 | 0 | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | − | 3.00000i | 0 | |||||||||||||||||||||||
607.2 | 0.707107 | − | 0.707107i | 0 | − | 1.00000i | 0 | 0 | 1.00000 | + | 1.00000i | −0.707107 | − | 0.707107i | − | 3.00000i | 0 | |||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.c | odd | 4 | 1 | inner |
19.b | odd | 2 | 1 | inner |
95.g | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 950.2.f.a | 4 | |
5.b | even | 2 | 1 | 190.2.f.a | ✓ | 4 | |
5.c | odd | 4 | 1 | 190.2.f.a | ✓ | 4 | |
5.c | odd | 4 | 1 | inner | 950.2.f.a | 4 | |
15.d | odd | 2 | 1 | 1710.2.p.a | 4 | ||
15.e | even | 4 | 1 | 1710.2.p.a | 4 | ||
19.b | odd | 2 | 1 | inner | 950.2.f.a | 4 | |
95.d | odd | 2 | 1 | 190.2.f.a | ✓ | 4 | |
95.g | even | 4 | 1 | 190.2.f.a | ✓ | 4 | |
95.g | even | 4 | 1 | inner | 950.2.f.a | 4 | |
285.b | even | 2 | 1 | 1710.2.p.a | 4 | ||
285.j | odd | 4 | 1 | 1710.2.p.a | 4 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
190.2.f.a | ✓ | 4 | 5.b | even | 2 | 1 | |
190.2.f.a | ✓ | 4 | 5.c | odd | 4 | 1 | |
190.2.f.a | ✓ | 4 | 95.d | odd | 2 | 1 | |
190.2.f.a | ✓ | 4 | 95.g | even | 4 | 1 | |
950.2.f.a | 4 | 1.a | even | 1 | 1 | trivial | |
950.2.f.a | 4 | 5.c | odd | 4 | 1 | inner | |
950.2.f.a | 4 | 19.b | odd | 2 | 1 | inner | |
950.2.f.a | 4 | 95.g | even | 4 | 1 | inner | |
1710.2.p.a | 4 | 15.d | odd | 2 | 1 | ||
1710.2.p.a | 4 | 15.e | even | 4 | 1 | ||
1710.2.p.a | 4 | 285.b | even | 2 | 1 | ||
1710.2.p.a | 4 | 285.j | odd | 4 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .