Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [308,3,Mod(83,308)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(308, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 5, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("308.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 308.s (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: | 8.0.37515625.1 |
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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83.1 |
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−1.99109 | + | 0.188551i | 0 | 3.92890 | − | 0.750845i | 0 | 0 | 5.66312 | − | 4.11450i | −7.68122 | + | 2.23580i | −2.78115 | − | 8.55951i | 0 | ||||||||||||||||||||||||||||||||
83.2 | −0.435959 | − | 1.95191i | 0 | −3.61988 | + | 1.70190i | 0 | 0 | 5.66312 | − | 4.11450i | 4.90007 | + | 6.32371i | −2.78115 | − | 8.55951i | 0 | |||||||||||||||||||||||||||||||||
139.1 | −0.794604 | − | 1.83538i | 0 | −2.73721 | + | 2.91679i | 0 | 0 | −2.16312 | − | 6.65740i | 7.52841 | + | 2.70611i | 7.28115 | + | 5.29007i | 0 | |||||||||||||||||||||||||||||||||
139.2 | 1.72166 | − | 1.01779i | 0 | 1.92819 | − | 3.50458i | 0 | 0 | −2.16312 | − | 6.65740i | −0.247258 | − | 7.99618i | 7.28115 | + | 5.29007i | 0 | |||||||||||||||||||||||||||||||||
167.1 | −1.99109 | − | 0.188551i | 0 | 3.92890 | + | 0.750845i | 0 | 0 | 5.66312 | + | 4.11450i | −7.68122 | − | 2.23580i | −2.78115 | + | 8.55951i | 0 | |||||||||||||||||||||||||||||||||
167.2 | −0.435959 | + | 1.95191i | 0 | −3.61988 | − | 1.70190i | 0 | 0 | 5.66312 | + | 4.11450i | 4.90007 | − | 6.32371i | −2.78115 | + | 8.55951i | 0 | |||||||||||||||||||||||||||||||||
195.1 | −0.794604 | + | 1.83538i | 0 | −2.73721 | − | 2.91679i | 0 | 0 | −2.16312 | + | 6.65740i | 7.52841 | − | 2.70611i | 7.28115 | − | 5.29007i | 0 | |||||||||||||||||||||||||||||||||
195.2 | 1.72166 | + | 1.01779i | 0 | 1.92819 | + | 3.50458i | 0 | 0 | −2.16312 | + | 6.65740i | −0.247258 | + | 7.99618i | 7.28115 | − | 5.29007i | 0 | |||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.b | odd | 2 | 1 | CM by |
44.g | even | 10 | 1 | inner |
308.s | odd | 10 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 308.3.s.a | ✓ | 8 |
4.b | odd | 2 | 1 | 308.3.s.b | yes | 8 | |
7.b | odd | 2 | 1 | CM | 308.3.s.a | ✓ | 8 |
11.d | odd | 10 | 1 | 308.3.s.b | yes | 8 | |
28.d | even | 2 | 1 | 308.3.s.b | yes | 8 | |
44.g | even | 10 | 1 | inner | 308.3.s.a | ✓ | 8 |
77.l | even | 10 | 1 | 308.3.s.b | yes | 8 | |
308.s | odd | 10 | 1 | inner | 308.3.s.a | ✓ | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
308.3.s.a | ✓ | 8 | 1.a | even | 1 | 1 | trivial |
308.3.s.a | ✓ | 8 | 7.b | odd | 2 | 1 | CM |
308.3.s.a | ✓ | 8 | 44.g | even | 10 | 1 | inner |
308.3.s.a | ✓ | 8 | 308.s | odd | 10 | 1 | inner |
308.3.s.b | yes | 8 | 4.b | odd | 2 | 1 | |
308.3.s.b | yes | 8 | 11.d | odd | 10 | 1 | |
308.3.s.b | yes | 8 | 28.d | even | 2 | 1 | |
308.3.s.b | yes | 8 | 77.l | even | 10 | 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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