Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [543,2,Mod(1,543)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(543, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("543.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 543.a (trivial) |
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: | yes |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Fricke sign: | |
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
:
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 |
|
−2.09416 | −1.00000 | 2.38551 | 1.57030 | 2.09416 | −3.68416 | −0.807326 | 1.00000 | −3.28847 | ||||||||||||||||||||||||||||||||||||||||||
1.2 | −1.57409 | −1.00000 | 0.477759 | 2.61079 | 1.57409 | 3.43627 | 2.39614 | 1.00000 | −4.10962 | |||||||||||||||||||||||||||||||||||||||||||
1.3 | −0.330181 | −1.00000 | −1.89098 | −3.90200 | 0.330181 | −4.54089 | 1.28473 | 1.00000 | 1.28837 | |||||||||||||||||||||||||||||||||||||||||||
1.4 | 0.216541 | −1.00000 | −1.95311 | −1.13532 | −0.216541 | 1.21084 | −0.856012 | 1.00000 | −0.245843 | |||||||||||||||||||||||||||||||||||||||||||
1.5 | 0.495668 | −1.00000 | −1.75431 | 3.58208 | −0.495668 | −1.17967 | −1.86089 | 1.00000 | 1.77552 | |||||||||||||||||||||||||||||||||||||||||||
1.6 | 1.49117 | −1.00000 | 0.223595 | −1.54064 | −1.49117 | 2.68646 | −2.64893 | 1.00000 | −2.29736 | |||||||||||||||||||||||||||||||||||||||||||
1.7 | 2.31010 | −1.00000 | 3.33658 | 3.44398 | −2.31010 | 1.03443 | 3.08764 | 1.00000 | 7.95596 | |||||||||||||||||||||||||||||||||||||||||||
1.8 | 2.48495 | −1.00000 | 4.17495 | 0.370811 | −2.48495 | −1.96328 | 5.40464 | 1.00000 | 0.921444 | |||||||||||||||||||||||||||||||||||||||||||
Atkin-Lehner signs
Sign | |
---|---|
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 543.2.a.d | ✓ | 8 |
3.b | odd | 2 | 1 | 1629.2.a.e | 8 | ||
4.b | odd | 2 | 1 | 8688.2.a.bf | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
543.2.a.d | ✓ | 8 | 1.a | even | 1 | 1 | trivial |
1629.2.a.e | 8 | 3.b | odd | 2 | 1 | ||
8688.2.a.bf | 8 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .