Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5994,2,Mod(1,5994)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5994, 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("5994.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 5994.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
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Defining polynomial: |
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Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 666) |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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1.1 |
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−1.00000 | 0 | 1.00000 | −3.69049 | 0 | 0.539128 | −1.00000 | 0 | 3.69049 | ||||||||||||||||||||||||||||||||||||||||||||||||
1.2 | −1.00000 | 0 | 1.00000 | −3.49123 | 0 | 2.86107 | −1.00000 | 0 | 3.49123 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.3 | −1.00000 | 0 | 1.00000 | −3.28277 | 0 | −3.13291 | −1.00000 | 0 | 3.28277 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.4 | −1.00000 | 0 | 1.00000 | −1.43355 | 0 | 0.697985 | −1.00000 | 0 | 1.43355 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.5 | −1.00000 | 0 | 1.00000 | −0.0738674 | 0 | 4.67803 | −1.00000 | 0 | 0.0738674 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.6 | −1.00000 | 0 | 1.00000 | 0.363318 | 0 | −5.03822 | −1.00000 | 0 | −0.363318 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.7 | −1.00000 | 0 | 1.00000 | 0.949474 | 0 | −4.04317 | −1.00000 | 0 | −0.949474 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.8 | −1.00000 | 0 | 1.00000 | 2.84378 | 0 | −0.483762 | −1.00000 | 0 | −2.84378 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.9 | −1.00000 | 0 | 1.00000 | 3.33861 | 0 | 0.195962 | −1.00000 | 0 | −3.33861 | |||||||||||||||||||||||||||||||||||||||||||||||||
1.10 | −1.00000 | 0 | 1.00000 | 3.47672 | 0 | 4.72589 | −1.00000 | 0 | −3.47672 | |||||||||||||||||||||||||||||||||||||||||||||||||
Atkin-Lehner signs
Sign | |
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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 | 5994.2.a.ba | 10 | |
3.b | odd | 2 | 1 | 5994.2.a.bb | 10 | ||
9.c | even | 3 | 2 | 1998.2.e.e | 20 | ||
9.d | odd | 6 | 2 | 666.2.e.e | ✓ | 20 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
666.2.e.e | ✓ | 20 | 9.d | odd | 6 | 2 | |
1998.2.e.e | 20 | 9.c | even | 3 | 2 | ||
5994.2.a.ba | 10 | 1.a | even | 1 | 1 | trivial | |
5994.2.a.bb | 10 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on :
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