Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1444,2,Mod(429,1444)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1444.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1444.e (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: | |
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 76) |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
429.1 |
|
0 | −1.34598 | + | 2.33131i | 0 | 0.641102 | − | 1.11042i | 0 | −3.34467 | 0 | −2.12333 | − | 3.67771i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||
429.2 | 0 | −0.544440 | + | 0.942998i | 0 | 1.60017 | − | 2.77158i | 0 | −0.556791 | 0 | 0.907170 | + | 1.57126i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
429.3 | 0 | −0.243160 | + | 0.421165i | 0 | −1.39668 | + | 2.41913i | 0 | −3.36570 | 0 | 1.38175 | + | 2.39326i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
429.4 | 0 | 0.906288 | − | 1.56974i | 0 | −0.141102 | + | 0.244396i | 0 | 1.15987 | 0 | −0.142716 | − | 0.247192i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
429.5 | 0 | 1.21809 | − | 2.10979i | 0 | −1.10017 | + | 1.90556i | 0 | 2.96827 | 0 | −1.46748 | − | 2.54175i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
429.6 | 0 | 1.50920 | − | 2.61402i | 0 | 1.89668 | − | 3.28515i | 0 | 0.139023 | 0 | −3.05539 | − | 5.29210i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.1 | 0 | −1.34598 | − | 2.33131i | 0 | 0.641102 | + | 1.11042i | 0 | −3.34467 | 0 | −2.12333 | + | 3.67771i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.2 | 0 | −0.544440 | − | 0.942998i | 0 | 1.60017 | + | 2.77158i | 0 | −0.556791 | 0 | 0.907170 | − | 1.57126i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.3 | 0 | −0.243160 | − | 0.421165i | 0 | −1.39668 | − | 2.41913i | 0 | −3.36570 | 0 | 1.38175 | − | 2.39326i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.4 | 0 | 0.906288 | + | 1.56974i | 0 | −0.141102 | − | 0.244396i | 0 | 1.15987 | 0 | −0.142716 | + | 0.247192i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.5 | 0 | 1.21809 | + | 2.10979i | 0 | −1.10017 | − | 1.90556i | 0 | 2.96827 | 0 | −1.46748 | + | 2.54175i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
653.6 | 0 | 1.50920 | + | 2.61402i | 0 | 1.89668 | + | 3.28515i | 0 | 0.139023 | 0 | −3.05539 | + | 5.29210i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.c | even | 3 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1444.2.e.h | 12 | |
19.b | odd | 2 | 1 | 1444.2.e.g | 12 | ||
19.c | even | 3 | 1 | 1444.2.a.g | 6 | ||
19.c | even | 3 | 1 | inner | 1444.2.e.h | 12 | |
19.d | odd | 6 | 1 | 1444.2.a.h | 6 | ||
19.d | odd | 6 | 1 | 1444.2.e.g | 12 | ||
19.f | odd | 18 | 2 | 76.2.i.a | ✓ | 12 | |
57.j | even | 18 | 2 | 684.2.bo.c | 12 | ||
76.f | even | 6 | 1 | 5776.2.a.bw | 6 | ||
76.g | odd | 6 | 1 | 5776.2.a.by | 6 | ||
76.k | even | 18 | 2 | 304.2.u.e | 12 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
76.2.i.a | ✓ | 12 | 19.f | odd | 18 | 2 | |
304.2.u.e | 12 | 76.k | even | 18 | 2 | ||
684.2.bo.c | 12 | 57.j | even | 18 | 2 | ||
1444.2.a.g | 6 | 19.c | even | 3 | 1 | ||
1444.2.a.h | 6 | 19.d | odd | 6 | 1 | ||
1444.2.e.g | 12 | 19.b | odd | 2 | 1 | ||
1444.2.e.g | 12 | 19.d | odd | 6 | 1 | ||
1444.2.e.h | 12 | 1.a | even | 1 | 1 | trivial | |
1444.2.e.h | 12 | 19.c | even | 3 | 1 | inner | |
5776.2.a.bw | 6 | 76.f | even | 6 | 1 | ||
5776.2.a.by | 6 | 76.g | odd | 6 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .