Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,3,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 74.g (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: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
23.1 |
|
−0.366025 | − | 1.36603i | −2.05446 | + | 1.18614i | −1.73205 | + | 1.00000i | −1.44602 | + | 5.39662i | 2.37228 | + | 2.37228i | 2.26217 | + | 3.91819i | 2.00000 | + | 2.00000i | −1.68614 | + | 2.92048i | 7.90120 | ||||||||||||||||||||||||||
23.2 | −0.366025 | − | 1.36603i | 2.92048 | − | 1.68614i | −1.73205 | + | 1.00000i | 0.981918 | − | 3.66457i | −3.37228 | − | 3.37228i | 0.603857 | + | 1.04591i | 2.00000 | + | 2.00000i | 1.18614 | − | 2.05446i | −5.36530 | |||||||||||||||||||||||||||
29.1 | −0.366025 | + | 1.36603i | −2.05446 | − | 1.18614i | −1.73205 | − | 1.00000i | −1.44602 | − | 5.39662i | 2.37228 | − | 2.37228i | 2.26217 | − | 3.91819i | 2.00000 | − | 2.00000i | −1.68614 | − | 2.92048i | 7.90120 | |||||||||||||||||||||||||||
29.2 | −0.366025 | + | 1.36603i | 2.92048 | + | 1.68614i | −1.73205 | − | 1.00000i | 0.981918 | + | 3.66457i | −3.37228 | + | 3.37228i | 0.603857 | − | 1.04591i | 2.00000 | − | 2.00000i | 1.18614 | + | 2.05446i | −5.36530 | |||||||||||||||||||||||||||
45.1 | 1.36603 | + | 0.366025i | −2.92048 | − | 1.68614i | 1.73205 | + | 1.00000i | 7.76264 | − | 2.07999i | −3.37228 | − | 3.37228i | 1.39614 | − | 2.41819i | 2.00000 | + | 2.00000i | 1.18614 | + | 2.05446i | 11.3653 | |||||||||||||||||||||||||||
45.2 | 1.36603 | + | 0.366025i | 2.05446 | + | 1.18614i | 1.73205 | + | 1.00000i | −1.29854 | + | 0.347944i | 2.37228 | + | 2.37228i | −0.262169 | + | 0.454090i | 2.00000 | + | 2.00000i | −1.68614 | − | 2.92048i | −1.90120 | |||||||||||||||||||||||||||
51.1 | 1.36603 | − | 0.366025i | −2.92048 | + | 1.68614i | 1.73205 | − | 1.00000i | 7.76264 | + | 2.07999i | −3.37228 | + | 3.37228i | 1.39614 | + | 2.41819i | 2.00000 | − | 2.00000i | 1.18614 | − | 2.05446i | 11.3653 | |||||||||||||||||||||||||||
51.2 | 1.36603 | − | 0.366025i | 2.05446 | − | 1.18614i | 1.73205 | − | 1.00000i | −1.29854 | − | 0.347944i | 2.37228 | − | 2.37228i | −0.262169 | − | 0.454090i | 2.00000 | − | 2.00000i | −1.68614 | + | 2.92048i | −1.90120 | |||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
37.g | odd | 12 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 74.3.g.a | ✓ | 8 |
37.g | odd | 12 | 1 | inner | 74.3.g.a | ✓ | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
74.3.g.a | ✓ | 8 | 1.a | even | 1 | 1 | trivial |
74.3.g.a | ✓ | 8 | 37.g | odd | 12 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .