Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(91,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 460.e (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: | |
Coefficient field: | 16.0.7465802011608416256.3 |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
91.1 |
|
−1.35760 | − | 0.396143i | 1.47175i | 1.68614 | + | 1.07561i | − | 1.00000i | 0.583024 | − | 1.99804i | −3.53986 | −1.86301 | − | 2.12819i | 0.833952 | −0.396143 | + | 1.35760i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.2 | −1.35760 | − | 0.396143i | 1.47175i | 1.68614 | + | 1.07561i | 1.00000i | 0.583024 | − | 1.99804i | 3.53986 | −1.86301 | − | 2.12819i | 0.833952 | 0.396143 | − | 1.35760i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.3 | −1.35760 | + | 0.396143i | − | 1.47175i | 1.68614 | − | 1.07561i | − | 1.00000i | 0.583024 | + | 1.99804i | 3.53986 | −1.86301 | + | 2.12819i | 0.833952 | 0.396143 | + | 1.35760i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.4 | −1.35760 | + | 0.396143i | − | 1.47175i | 1.68614 | − | 1.07561i | 1.00000i | 0.583024 | + | 1.99804i | −3.53986 | −1.86301 | + | 2.12819i | 0.833952 | −0.396143 | − | 1.35760i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.5 | −0.637910 | − | 1.26217i | 2.87247i | −1.18614 | + | 1.61030i | − | 1.00000i | 3.62554 | − | 1.83238i | −2.68161 | 2.78912 | + | 0.469882i | −5.25109 | −1.26217 | + | 0.637910i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.6 | −0.637910 | − | 1.26217i | 2.87247i | −1.18614 | + | 1.61030i | 1.00000i | 3.62554 | − | 1.83238i | 2.68161 | 2.78912 | + | 0.469882i | −5.25109 | 1.26217 | − | 0.637910i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.7 | −0.637910 | + | 1.26217i | − | 2.87247i | −1.18614 | − | 1.61030i | − | 1.00000i | 3.62554 | + | 1.83238i | 2.68161 | 2.78912 | − | 0.469882i | −5.25109 | 1.26217 | + | 0.637910i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.8 | −0.637910 | + | 1.26217i | − | 2.87247i | −1.18614 | − | 1.61030i | 1.00000i | 3.62554 | + | 1.83238i | −2.68161 | 2.78912 | − | 0.469882i | −5.25109 | −1.26217 | − | 0.637910i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.9 | 0.637910 | − | 1.26217i | − | 0.348132i | −1.18614 | − | 1.61030i | − | 1.00000i | −0.439402 | − | 0.222077i | −4.89140 | −2.78912 | + | 0.469882i | 2.87880 | −1.26217 | − | 0.637910i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.10 | 0.637910 | − | 1.26217i | − | 0.348132i | −1.18614 | − | 1.61030i | 1.00000i | −0.439402 | − | 0.222077i | 4.89140 | −2.78912 | + | 0.469882i | 2.87880 | 1.26217 | + | 0.637910i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.11 | 0.637910 | + | 1.26217i | 0.348132i | −1.18614 | + | 1.61030i | − | 1.00000i | −0.439402 | + | 0.222077i | 4.89140 | −2.78912 | − | 0.469882i | 2.87880 | 1.26217 | − | 0.637910i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.12 | 0.637910 | + | 1.26217i | 0.348132i | −1.18614 | + | 1.61030i | 1.00000i | −0.439402 | + | 0.222077i | −4.89140 | −2.78912 | − | 0.469882i | 2.87880 | −1.26217 | + | 0.637910i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.13 | 1.35760 | − | 0.396143i | − | 0.679463i | 1.68614 | − | 1.07561i | − | 1.00000i | −0.269165 | − | 0.922437i | 1.16300 | 1.86301 | − | 2.12819i | 2.53833 | −0.396143 | − | 1.35760i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.14 | 1.35760 | − | 0.396143i | − | 0.679463i | 1.68614 | − | 1.07561i | 1.00000i | −0.269165 | − | 0.922437i | −1.16300 | 1.86301 | − | 2.12819i | 2.53833 | 0.396143 | + | 1.35760i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.15 | 1.35760 | + | 0.396143i | 0.679463i | 1.68614 | + | 1.07561i | − | 1.00000i | −0.269165 | + | 0.922437i | −1.16300 | 1.86301 | + | 2.12819i | 2.53833 | 0.396143 | − | 1.35760i | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91.16 | 1.35760 | + | 0.396143i | 0.679463i | 1.68614 | + | 1.07561i | 1.00000i | −0.269165 | + | 0.922437i | 1.16300 | 1.86301 | + | 2.12819i | 2.53833 | −0.396143 | + | 1.35760i | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
4.b | odd | 2 | 1 | inner |
23.b | odd | 2 | 1 | inner |
92.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 460.2.e.a | ✓ | 16 |
4.b | odd | 2 | 1 | inner | 460.2.e.a | ✓ | 16 |
23.b | odd | 2 | 1 | inner | 460.2.e.a | ✓ | 16 |
92.b | even | 2 | 1 | inner | 460.2.e.a | ✓ | 16 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
460.2.e.a | ✓ | 16 | 1.a | even | 1 | 1 | trivial |
460.2.e.a | ✓ | 16 | 4.b | odd | 2 | 1 | inner |
460.2.e.a | ✓ | 16 | 23.b | odd | 2 | 1 | inner |
460.2.e.a | ✓ | 16 | 92.b | even | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .