Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3168,2,Mod(2287,3168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3168, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("3168.2287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 3168.h (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: | 16.0.3342602057661458415616.4 |
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 792) |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2287.1 |
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0 | 0 | 0 | − | 2.00000i | 0 | −3.02045 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.2 | 0 | 0 | 0 | − | 2.00000i | 0 | −3.02045 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.3 | 0 | 0 | 0 | − | 2.00000i | 0 | −0.936426 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.4 | 0 | 0 | 0 | − | 2.00000i | 0 | −0.936426 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.5 | 0 | 0 | 0 | − | 2.00000i | 0 | 0.936426 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.6 | 0 | 0 | 0 | − | 2.00000i | 0 | 0.936426 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.7 | 0 | 0 | 0 | − | 2.00000i | 0 | 3.02045 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.8 | 0 | 0 | 0 | − | 2.00000i | 0 | 3.02045 | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.9 | 0 | 0 | 0 | 2.00000i | 0 | −3.02045 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.10 | 0 | 0 | 0 | 2.00000i | 0 | −3.02045 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.11 | 0 | 0 | 0 | 2.00000i | 0 | −0.936426 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.12 | 0 | 0 | 0 | 2.00000i | 0 | −0.936426 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.13 | 0 | 0 | 0 | 2.00000i | 0 | 0.936426 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.14 | 0 | 0 | 0 | 2.00000i | 0 | 0.936426 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.15 | 0 | 0 | 0 | 2.00000i | 0 | 3.02045 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2287.16 | 0 | 0 | 0 | 2.00000i | 0 | 3.02045 | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
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1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
8.d | odd | 2 | 1 | inner |
11.b | odd | 2 | 1 | inner |
24.f | even | 2 | 1 | inner |
33.d | even | 2 | 1 | inner |
88.g | even | 2 | 1 | inner |
264.p | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 3168.2.h.i | 16 | |
3.b | odd | 2 | 1 | inner | 3168.2.h.i | 16 | |
4.b | odd | 2 | 1 | 792.2.h.i | ✓ | 16 | |
8.b | even | 2 | 1 | 792.2.h.i | ✓ | 16 | |
8.d | odd | 2 | 1 | inner | 3168.2.h.i | 16 | |
11.b | odd | 2 | 1 | inner | 3168.2.h.i | 16 | |
12.b | even | 2 | 1 | 792.2.h.i | ✓ | 16 | |
24.f | even | 2 | 1 | inner | 3168.2.h.i | 16 | |
24.h | odd | 2 | 1 | 792.2.h.i | ✓ | 16 | |
33.d | even | 2 | 1 | inner | 3168.2.h.i | 16 | |
44.c | even | 2 | 1 | 792.2.h.i | ✓ | 16 | |
88.b | odd | 2 | 1 | 792.2.h.i | ✓ | 16 | |
88.g | even | 2 | 1 | inner | 3168.2.h.i | 16 | |
132.d | odd | 2 | 1 | 792.2.h.i | ✓ | 16 | |
264.m | even | 2 | 1 | 792.2.h.i | ✓ | 16 | |
264.p | odd | 2 | 1 | inner | 3168.2.h.i | 16 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
792.2.h.i | ✓ | 16 | 4.b | odd | 2 | 1 | |
792.2.h.i | ✓ | 16 | 8.b | even | 2 | 1 | |
792.2.h.i | ✓ | 16 | 12.b | even | 2 | 1 | |
792.2.h.i | ✓ | 16 | 24.h | odd | 2 | 1 | |
792.2.h.i | ✓ | 16 | 44.c | even | 2 | 1 | |
792.2.h.i | ✓ | 16 | 88.b | odd | 2 | 1 | |
792.2.h.i | ✓ | 16 | 132.d | odd | 2 | 1 | |
792.2.h.i | ✓ | 16 | 264.m | even | 2 | 1 | |
3168.2.h.i | 16 | 1.a | even | 1 | 1 | trivial | |
3168.2.h.i | 16 | 3.b | odd | 2 | 1 | inner | |
3168.2.h.i | 16 | 8.d | odd | 2 | 1 | inner | |
3168.2.h.i | 16 | 11.b | odd | 2 | 1 | inner | |
3168.2.h.i | 16 | 24.f | even | 2 | 1 | inner | |
3168.2.h.i | 16 | 33.d | even | 2 | 1 | inner | |
3168.2.h.i | 16 | 88.g | even | 2 | 1 | inner | |
3168.2.h.i | 16 | 264.p | odd | 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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