Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(31,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1520.bq (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: | 8.0.1121513121.1 |
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: | 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
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31.1 |
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0 | −1.17747 | − | 2.03944i | 0 | −0.500000 | − | 0.866025i | 0 | 3.23155i | 0 | −1.27288 | + | 2.20470i | 0 | ||||||||||||||||||||||||||||||||||||
31.2 | 0 | −0.341612 | − | 0.591690i | 0 | −0.500000 | − | 0.866025i | 0 | − | 4.79806i | 0 | 1.26660 | − | 2.19382i | 0 | ||||||||||||||||||||||||||||||||||||
31.3 | 0 | 0.110293 | + | 0.191033i | 0 | −0.500000 | − | 0.866025i | 0 | 1.12206i | 0 | 1.47567 | − | 2.55594i | 0 | |||||||||||||||||||||||||||||||||||||
31.4 | 0 | 1.40879 | + | 2.44010i | 0 | −0.500000 | − | 0.866025i | 0 | 3.90855i | 0 | −2.46939 | + | 4.27711i | 0 | |||||||||||||||||||||||||||||||||||||
1471.1 | 0 | −1.17747 | + | 2.03944i | 0 | −0.500000 | + | 0.866025i | 0 | − | 3.23155i | 0 | −1.27288 | − | 2.20470i | 0 | ||||||||||||||||||||||||||||||||||||
1471.2 | 0 | −0.341612 | + | 0.591690i | 0 | −0.500000 | + | 0.866025i | 0 | 4.79806i | 0 | 1.26660 | + | 2.19382i | 0 | |||||||||||||||||||||||||||||||||||||
1471.3 | 0 | 0.110293 | − | 0.191033i | 0 | −0.500000 | + | 0.866025i | 0 | − | 1.12206i | 0 | 1.47567 | + | 2.55594i | 0 | ||||||||||||||||||||||||||||||||||||
1471.4 | 0 | 1.40879 | − | 2.44010i | 0 | −0.500000 | + | 0.866025i | 0 | − | 3.90855i | 0 | −2.46939 | − | 4.27711i | 0 | ||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
76.f | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
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Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1520.2.bq.p | yes | 8 |
4.b | odd | 2 | 1 | 1520.2.bq.o | ✓ | 8 | |
19.d | odd | 6 | 1 | 1520.2.bq.o | ✓ | 8 | |
76.f | even | 6 | 1 | inner | 1520.2.bq.p | yes | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1520.2.bq.o | ✓ | 8 | 4.b | odd | 2 | 1 | |
1520.2.bq.o | ✓ | 8 | 19.d | odd | 6 | 1 | |
1520.2.bq.p | yes | 8 | 1.a | even | 1 | 1 | trivial |
1520.2.bq.p | yes | 8 | 76.f | even | 6 | 1 | inner |
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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