Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(449,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1120.g (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: | 10.0.65174749855744.1 |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
449.1 |
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0 | − | 3.25260i | 0 | −1.49436 | + | 1.66340i | 0 | − | 1.00000i | 0 | −7.57939 | 0 | ||||||||||||||||||||||||||||||||||||||||||||
449.2 | 0 | − | 2.19794i | 0 | 1.64514 | − | 1.51444i | 0 | 1.00000i | 0 | −1.83094 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||
449.3 | 0 | − | 1.83297i | 0 | 1.86302 | − | 1.23660i | 0 | − | 1.00000i | 0 | −0.359777 | 0 | |||||||||||||||||||||||||||||||||||||||||||||
449.4 | 0 | − | 1.63460i | 0 | −2.23081 | − | 0.153266i | 0 | 1.00000i | 0 | 0.328072 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||
449.5 | 0 | − | 0.746976i | 0 | −0.782984 | − | 2.09450i | 0 | − | 1.00000i | 0 | 2.44203 | 0 | |||||||||||||||||||||||||||||||||||||||||||||
449.6 | 0 | 0.746976i | 0 | −0.782984 | + | 2.09450i | 0 | 1.00000i | 0 | 2.44203 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||
449.7 | 0 | 1.63460i | 0 | −2.23081 | + | 0.153266i | 0 | − | 1.00000i | 0 | 0.328072 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||
449.8 | 0 | 1.83297i | 0 | 1.86302 | + | 1.23660i | 0 | 1.00000i | 0 | −0.359777 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||
449.9 | 0 | 2.19794i | 0 | 1.64514 | + | 1.51444i | 0 | − | 1.00000i | 0 | −1.83094 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||
449.10 | 0 | 3.25260i | 0 | −1.49436 | − | 1.66340i | 0 | 1.00000i | 0 | −7.57939 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1120.2.g.b | ✓ | 10 |
4.b | odd | 2 | 1 | 1120.2.g.c | yes | 10 | |
5.b | even | 2 | 1 | inner | 1120.2.g.b | ✓ | 10 |
5.c | odd | 4 | 1 | 5600.2.a.bu | 5 | ||
5.c | odd | 4 | 1 | 5600.2.a.bw | 5 | ||
8.b | even | 2 | 1 | 2240.2.g.o | 10 | ||
8.d | odd | 2 | 1 | 2240.2.g.n | 10 | ||
20.d | odd | 2 | 1 | 1120.2.g.c | yes | 10 | |
20.e | even | 4 | 1 | 5600.2.a.bv | 5 | ||
20.e | even | 4 | 1 | 5600.2.a.bx | 5 | ||
40.e | odd | 2 | 1 | 2240.2.g.n | 10 | ||
40.f | even | 2 | 1 | 2240.2.g.o | 10 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1120.2.g.b | ✓ | 10 | 1.a | even | 1 | 1 | trivial |
1120.2.g.b | ✓ | 10 | 5.b | even | 2 | 1 | inner |
1120.2.g.c | yes | 10 | 4.b | odd | 2 | 1 | |
1120.2.g.c | yes | 10 | 20.d | odd | 2 | 1 | |
2240.2.g.n | 10 | 8.d | odd | 2 | 1 | ||
2240.2.g.n | 10 | 40.e | odd | 2 | 1 | ||
2240.2.g.o | 10 | 8.b | even | 2 | 1 | ||
2240.2.g.o | 10 | 40.f | even | 2 | 1 | ||
5600.2.a.bu | 5 | 5.c | odd | 4 | 1 | ||
5600.2.a.bv | 5 | 20.e | even | 4 | 1 | ||
5600.2.a.bw | 5 | 5.c | odd | 4 | 1 | ||
5600.2.a.bx | 5 | 20.e | even | 4 | 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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