Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1680.f (of order , degree , not 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: | |
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 105) |
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 | ||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
881.1 |
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0 | −1.18614 | − | 1.26217i | 0 | −1.00000 | 0 | 2.00000 | − | 1.73205i | 0 | −0.186141 | + | 2.99422i | 0 | ||||||||||||||||||||||||
881.2 | 0 | −1.18614 | + | 1.26217i | 0 | −1.00000 | 0 | 2.00000 | + | 1.73205i | 0 | −0.186141 | − | 2.99422i | 0 | |||||||||||||||||||||||||
881.3 | 0 | 1.68614 | − | 0.396143i | 0 | −1.00000 | 0 | 2.00000 | + | 1.73205i | 0 | 2.68614 | − | 1.33591i | 0 | |||||||||||||||||||||||||
881.4 | 0 | 1.68614 | + | 0.396143i | 0 | −1.00000 | 0 | 2.00000 | − | 1.73205i | 0 | 2.68614 | + | 1.33591i | 0 | |||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
21.c | even | 2 | 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 | 1680.2.f.h | 4 | |
3.b | odd | 2 | 1 | 1680.2.f.g | 4 | ||
4.b | odd | 2 | 1 | 105.2.b.c | ✓ | 4 | |
7.b | odd | 2 | 1 | 1680.2.f.g | 4 | ||
12.b | even | 2 | 1 | 105.2.b.d | yes | 4 | |
20.d | odd | 2 | 1 | 525.2.b.g | 4 | ||
20.e | even | 4 | 2 | 525.2.g.e | 8 | ||
21.c | even | 2 | 1 | inner | 1680.2.f.h | 4 | |
28.d | even | 2 | 1 | 105.2.b.d | yes | 4 | |
28.f | even | 6 | 1 | 735.2.s.g | 4 | ||
28.f | even | 6 | 1 | 735.2.s.j | 4 | ||
28.g | odd | 6 | 1 | 735.2.s.h | 4 | ||
28.g | odd | 6 | 1 | 735.2.s.i | 4 | ||
60.h | even | 2 | 1 | 525.2.b.e | 4 | ||
60.l | odd | 4 | 2 | 525.2.g.d | 8 | ||
84.h | odd | 2 | 1 | 105.2.b.c | ✓ | 4 | |
84.j | odd | 6 | 1 | 735.2.s.h | 4 | ||
84.j | odd | 6 | 1 | 735.2.s.i | 4 | ||
84.n | even | 6 | 1 | 735.2.s.g | 4 | ||
84.n | even | 6 | 1 | 735.2.s.j | 4 | ||
140.c | even | 2 | 1 | 525.2.b.e | 4 | ||
140.j | odd | 4 | 2 | 525.2.g.d | 8 | ||
420.o | odd | 2 | 1 | 525.2.b.g | 4 | ||
420.w | even | 4 | 2 | 525.2.g.e | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
105.2.b.c | ✓ | 4 | 4.b | odd | 2 | 1 | |
105.2.b.c | ✓ | 4 | 84.h | odd | 2 | 1 | |
105.2.b.d | yes | 4 | 12.b | even | 2 | 1 | |
105.2.b.d | yes | 4 | 28.d | even | 2 | 1 | |
525.2.b.e | 4 | 60.h | even | 2 | 1 | ||
525.2.b.e | 4 | 140.c | even | 2 | 1 | ||
525.2.b.g | 4 | 20.d | odd | 2 | 1 | ||
525.2.b.g | 4 | 420.o | odd | 2 | 1 | ||
525.2.g.d | 8 | 60.l | odd | 4 | 2 | ||
525.2.g.d | 8 | 140.j | odd | 4 | 2 | ||
525.2.g.e | 8 | 20.e | even | 4 | 2 | ||
525.2.g.e | 8 | 420.w | even | 4 | 2 | ||
735.2.s.g | 4 | 28.f | even | 6 | 1 | ||
735.2.s.g | 4 | 84.n | even | 6 | 1 | ||
735.2.s.h | 4 | 28.g | odd | 6 | 1 | ||
735.2.s.h | 4 | 84.j | odd | 6 | 1 | ||
735.2.s.i | 4 | 28.g | odd | 6 | 1 | ||
735.2.s.i | 4 | 84.j | odd | 6 | 1 | ||
735.2.s.j | 4 | 28.f | even | 6 | 1 | ||
735.2.s.j | 4 | 84.n | even | 6 | 1 | ||
1680.2.f.g | 4 | 3.b | odd | 2 | 1 | ||
1680.2.f.g | 4 | 7.b | odd | 2 | 1 | ||
1680.2.f.h | 4 | 1.a | even | 1 | 1 | trivial | |
1680.2.f.h | 4 | 21.c | even | 2 | 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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