Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(1145,2548)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2548, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2548.1145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2548.j (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: | |
Relative dimension: | over |
Coefficient field: | 8.0.856615824.2 |
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 364) |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1145.1 |
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0 | −0.925606 | + | 1.60320i | 0 | 1.56470 | + | 2.71015i | 0 | 0 | 0 | −0.213493 | − | 0.369780i | 0 | ||||||||||||||||||||||||||||||||||||
1145.2 | 0 | −0.418594 | + | 0.725026i | 0 | −0.812371 | − | 1.40707i | 0 | 0 | 0 | 1.14956 | + | 1.99109i | 0 | |||||||||||||||||||||||||||||||||||||
1145.3 | 0 | 1.12774 | − | 1.95330i | 0 | −1.71189 | − | 2.96508i | 0 | 0 | 0 | −1.04359 | − | 1.80755i | 0 | |||||||||||||||||||||||||||||||||||||
1145.4 | 0 | 1.71646 | − | 2.97300i | 0 | 0.459555 | + | 0.795973i | 0 | 0 | 0 | −4.39248 | − | 7.60799i | 0 | |||||||||||||||||||||||||||||||||||||
1353.1 | 0 | −0.925606 | − | 1.60320i | 0 | 1.56470 | − | 2.71015i | 0 | 0 | 0 | −0.213493 | + | 0.369780i | 0 | |||||||||||||||||||||||||||||||||||||
1353.2 | 0 | −0.418594 | − | 0.725026i | 0 | −0.812371 | + | 1.40707i | 0 | 0 | 0 | 1.14956 | − | 1.99109i | 0 | |||||||||||||||||||||||||||||||||||||
1353.3 | 0 | 1.12774 | + | 1.95330i | 0 | −1.71189 | + | 2.96508i | 0 | 0 | 0 | −1.04359 | + | 1.80755i | 0 | |||||||||||||||||||||||||||||||||||||
1353.4 | 0 | 1.71646 | + | 2.97300i | 0 | 0.459555 | − | 0.795973i | 0 | 0 | 0 | −4.39248 | + | 7.60799i | 0 | |||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.c | even | 3 | 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 | 2548.2.j.q | 8 | |
7.b | odd | 2 | 1 | 364.2.j.e | ✓ | 8 | |
7.c | even | 3 | 1 | 2548.2.a.p | 4 | ||
7.c | even | 3 | 1 | inner | 2548.2.j.q | 8 | |
7.d | odd | 6 | 1 | 364.2.j.e | ✓ | 8 | |
7.d | odd | 6 | 1 | 2548.2.a.q | 4 | ||
21.c | even | 2 | 1 | 3276.2.r.j | 8 | ||
21.g | even | 6 | 1 | 3276.2.r.j | 8 | ||
28.d | even | 2 | 1 | 1456.2.r.o | 8 | ||
28.f | even | 6 | 1 | 1456.2.r.o | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
364.2.j.e | ✓ | 8 | 7.b | odd | 2 | 1 | |
364.2.j.e | ✓ | 8 | 7.d | odd | 6 | 1 | |
1456.2.r.o | 8 | 28.d | even | 2 | 1 | ||
1456.2.r.o | 8 | 28.f | even | 6 | 1 | ||
2548.2.a.p | 4 | 7.c | even | 3 | 1 | ||
2548.2.a.q | 4 | 7.d | odd | 6 | 1 | ||
2548.2.j.q | 8 | 1.a | even | 1 | 1 | trivial | |
2548.2.j.q | 8 | 7.c | even | 3 | 1 | inner | |
3276.2.r.j | 8 | 21.c | even | 2 | 1 | ||
3276.2.r.j | 8 | 21.g | even | 6 | 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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