Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(1151,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1280.g (of order , degree , not 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: | |
Coefficient field: | 8.0.12960000.1 |
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 80) |
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 basis for the coefficient ring described below. We also show the integral -expansion of the trace form.
Basis of coefficient ring in terms of a root of
:
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1151.1 |
|
0 | −5.60503 | 0 | − | 2.23607i | 0 | − | 1.32317i | 0 | 22.4164 | 0 | ||||||||||||||||||||||||||||||||||||||||
1151.2 | 0 | −5.60503 | 0 | 2.23607i | 0 | 1.32317i | 0 | 22.4164 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1151.3 | 0 | −2.14093 | 0 | − | 2.23607i | 0 | − | 9.06914i | 0 | −4.41641 | 0 | |||||||||||||||||||||||||||||||||||||||||
1151.4 | 0 | −2.14093 | 0 | 2.23607i | 0 | 9.06914i | 0 | −4.41641 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1151.5 | 0 | 2.14093 | 0 | − | 2.23607i | 0 | 9.06914i | 0 | −4.41641 | 0 | ||||||||||||||||||||||||||||||||||||||||||
1151.6 | 0 | 2.14093 | 0 | 2.23607i | 0 | − | 9.06914i | 0 | −4.41641 | 0 | ||||||||||||||||||||||||||||||||||||||||||
1151.7 | 0 | 5.60503 | 0 | − | 2.23607i | 0 | 1.32317i | 0 | 22.4164 | 0 | ||||||||||||||||||||||||||||||||||||||||||
1151.8 | 0 | 5.60503 | 0 | 2.23607i | 0 | − | 1.32317i | 0 | 22.4164 | 0 | ||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
4.b | odd | 2 | 1 | inner |
8.b | even | 2 | 1 | inner |
8.d | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1280.3.g.f | 8 | |
4.b | odd | 2 | 1 | inner | 1280.3.g.f | 8 | |
8.b | even | 2 | 1 | inner | 1280.3.g.f | 8 | |
8.d | odd | 2 | 1 | inner | 1280.3.g.f | 8 | |
16.e | even | 4 | 1 | 80.3.b.a | ✓ | 4 | |
16.e | even | 4 | 1 | 320.3.b.a | 4 | ||
16.f | odd | 4 | 1 | 80.3.b.a | ✓ | 4 | |
16.f | odd | 4 | 1 | 320.3.b.a | 4 | ||
48.i | odd | 4 | 1 | 720.3.e.c | 4 | ||
48.i | odd | 4 | 1 | 2880.3.e.b | 4 | ||
48.k | even | 4 | 1 | 720.3.e.c | 4 | ||
48.k | even | 4 | 1 | 2880.3.e.b | 4 | ||
80.i | odd | 4 | 1 | 400.3.h.d | 8 | ||
80.i | odd | 4 | 1 | 1600.3.h.p | 8 | ||
80.j | even | 4 | 1 | 400.3.h.d | 8 | ||
80.j | even | 4 | 1 | 1600.3.h.p | 8 | ||
80.k | odd | 4 | 1 | 400.3.b.g | 4 | ||
80.k | odd | 4 | 1 | 1600.3.b.k | 4 | ||
80.q | even | 4 | 1 | 400.3.b.g | 4 | ||
80.q | even | 4 | 1 | 1600.3.b.k | 4 | ||
80.s | even | 4 | 1 | 400.3.h.d | 8 | ||
80.s | even | 4 | 1 | 1600.3.h.p | 8 | ||
80.t | odd | 4 | 1 | 400.3.h.d | 8 | ||
80.t | odd | 4 | 1 | 1600.3.h.p | 8 | ||
240.t | even | 4 | 1 | 3600.3.e.bb | 4 | ||
240.z | odd | 4 | 1 | 3600.3.j.k | 8 | ||
240.bb | even | 4 | 1 | 3600.3.j.k | 8 | ||
240.bd | odd | 4 | 1 | 3600.3.j.k | 8 | ||
240.bf | even | 4 | 1 | 3600.3.j.k | 8 | ||
240.bm | odd | 4 | 1 | 3600.3.e.bb | 4 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
80.3.b.a | ✓ | 4 | 16.e | even | 4 | 1 | |
80.3.b.a | ✓ | 4 | 16.f | odd | 4 | 1 | |
320.3.b.a | 4 | 16.e | even | 4 | 1 | ||
320.3.b.a | 4 | 16.f | odd | 4 | 1 | ||
400.3.b.g | 4 | 80.k | odd | 4 | 1 | ||
400.3.b.g | 4 | 80.q | even | 4 | 1 | ||
400.3.h.d | 8 | 80.i | odd | 4 | 1 | ||
400.3.h.d | 8 | 80.j | even | 4 | 1 | ||
400.3.h.d | 8 | 80.s | even | 4 | 1 | ||
400.3.h.d | 8 | 80.t | odd | 4 | 1 | ||
720.3.e.c | 4 | 48.i | odd | 4 | 1 | ||
720.3.e.c | 4 | 48.k | even | 4 | 1 | ||
1280.3.g.f | 8 | 1.a | even | 1 | 1 | trivial | |
1280.3.g.f | 8 | 4.b | odd | 2 | 1 | inner | |
1280.3.g.f | 8 | 8.b | even | 2 | 1 | inner | |
1280.3.g.f | 8 | 8.d | odd | 2 | 1 | inner | |
1600.3.b.k | 4 | 80.k | odd | 4 | 1 | ||
1600.3.b.k | 4 | 80.q | even | 4 | 1 | ||
1600.3.h.p | 8 | 80.i | odd | 4 | 1 | ||
1600.3.h.p | 8 | 80.j | even | 4 | 1 | ||
1600.3.h.p | 8 | 80.s | even | 4 | 1 | ||
1600.3.h.p | 8 | 80.t | odd | 4 | 1 | ||
2880.3.e.b | 4 | 48.i | odd | 4 | 1 | ||
2880.3.e.b | 4 | 48.k | even | 4 | 1 | ||
3600.3.e.bb | 4 | 240.t | even | 4 | 1 | ||
3600.3.e.bb | 4 | 240.bm | odd | 4 | 1 | ||
3600.3.j.k | 8 | 240.z | odd | 4 | 1 | ||
3600.3.j.k | 8 | 240.bb | even | 4 | 1 | ||
3600.3.j.k | 8 | 240.bd | odd | 4 | 1 | ||
3600.3.j.k | 8 | 240.bf | even | 4 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .