Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(1151,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.1151");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1152.c (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: | |
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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1151.1 |
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0 | 0 | 0 | − | 19.4649i | 0 | 22.2014i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.2 | 0 | 0 | 0 | − | 15.9893i | 0 | 4.39346i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.3 | 0 | 0 | 0 | − | 12.9056i | 0 | − | 14.2604i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.4 | 0 | 0 | 0 | − | 9.77328i | 0 | 16.6123i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.5 | 0 | 0 | 0 | − | 1.63027i | 0 | − | 15.3904i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.6 | 0 | 0 | 0 | − | 0.854915i | 0 | − | 27.6333i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.7 | 0 | 0 | 0 | 0.854915i | 0 | 27.6333i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.8 | 0 | 0 | 0 | 1.63027i | 0 | 15.3904i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.9 | 0 | 0 | 0 | 9.77328i | 0 | − | 16.6123i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.10 | 0 | 0 | 0 | 12.9056i | 0 | 14.2604i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.11 | 0 | 0 | 0 | 15.9893i | 0 | − | 4.39346i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
1151.12 | 0 | 0 | 0 | 19.4649i | 0 | − | 22.2014i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
12.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1152.4.c.b | yes | 12 |
3.b | odd | 2 | 1 | 1152.4.c.c | yes | 12 | |
4.b | odd | 2 | 1 | 1152.4.c.c | yes | 12 | |
8.b | even | 2 | 1 | 1152.4.c.a | ✓ | 12 | |
8.d | odd | 2 | 1 | 1152.4.c.d | yes | 12 | |
12.b | even | 2 | 1 | inner | 1152.4.c.b | yes | 12 |
16.e | even | 4 | 1 | 2304.4.f.j | 12 | ||
16.e | even | 4 | 1 | 2304.4.f.l | 12 | ||
16.f | odd | 4 | 1 | 2304.4.f.i | 12 | ||
16.f | odd | 4 | 1 | 2304.4.f.k | 12 | ||
24.f | even | 2 | 1 | 1152.4.c.a | ✓ | 12 | |
24.h | odd | 2 | 1 | 1152.4.c.d | yes | 12 | |
48.i | odd | 4 | 1 | 2304.4.f.i | 12 | ||
48.i | odd | 4 | 1 | 2304.4.f.k | 12 | ||
48.k | even | 4 | 1 | 2304.4.f.j | 12 | ||
48.k | even | 4 | 1 | 2304.4.f.l | 12 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1152.4.c.a | ✓ | 12 | 8.b | even | 2 | 1 | |
1152.4.c.a | ✓ | 12 | 24.f | even | 2 | 1 | |
1152.4.c.b | yes | 12 | 1.a | even | 1 | 1 | trivial |
1152.4.c.b | yes | 12 | 12.b | even | 2 | 1 | inner |
1152.4.c.c | yes | 12 | 3.b | odd | 2 | 1 | |
1152.4.c.c | yes | 12 | 4.b | odd | 2 | 1 | |
1152.4.c.d | yes | 12 | 8.d | odd | 2 | 1 | |
1152.4.c.d | yes | 12 | 24.h | odd | 2 | 1 | |
2304.4.f.i | 12 | 16.f | odd | 4 | 1 | ||
2304.4.f.i | 12 | 48.i | odd | 4 | 1 | ||
2304.4.f.j | 12 | 16.e | even | 4 | 1 | ||
2304.4.f.j | 12 | 48.k | even | 4 | 1 | ||
2304.4.f.k | 12 | 16.f | odd | 4 | 1 | ||
2304.4.f.k | 12 | 48.i | odd | 4 | 1 | ||
2304.4.f.l | 12 | 16.e | even | 4 | 1 | ||
2304.4.f.l | 12 | 48.k | 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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