Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(165,2548)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2548.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2548.i (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: | |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
165.1 |
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0 | −1.31475 | − | 2.27721i | 0 | 0.934445 | + | 1.61851i | 0 | 0 | 0 | −1.95712 | + | 3.38982i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||
165.2 | 0 | −0.662644 | − | 1.14773i | 0 | −0.0919085 | − | 0.159190i | 0 | 0 | 0 | 0.621805 | − | 1.07700i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
165.3 | 0 | −0.286958 | − | 0.497025i | 0 | −1.45546 | − | 2.52093i | 0 | 0 | 0 | 1.33531 | − | 2.31283i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
165.4 | 0 | 0.286958 | + | 0.497025i | 0 | 1.45546 | + | 2.52093i | 0 | 0 | 0 | 1.33531 | − | 2.31283i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
165.5 | 0 | 0.662644 | + | 1.14773i | 0 | 0.0919085 | + | 0.159190i | 0 | 0 | 0 | 0.621805 | − | 1.07700i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
165.6 | 0 | 1.31475 | + | 2.27721i | 0 | −0.934445 | − | 1.61851i | 0 | 0 | 0 | −1.95712 | + | 3.38982i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.1 | 0 | −1.31475 | + | 2.27721i | 0 | 0.934445 | − | 1.61851i | 0 | 0 | 0 | −1.95712 | − | 3.38982i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.2 | 0 | −0.662644 | + | 1.14773i | 0 | −0.0919085 | + | 0.159190i | 0 | 0 | 0 | 0.621805 | + | 1.07700i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.3 | 0 | −0.286958 | + | 0.497025i | 0 | −1.45546 | + | 2.52093i | 0 | 0 | 0 | 1.33531 | + | 2.31283i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.4 | 0 | 0.286958 | − | 0.497025i | 0 | 1.45546 | − | 2.52093i | 0 | 0 | 0 | 1.33531 | + | 2.31283i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.5 | 0 | 0.662644 | − | 1.14773i | 0 | 0.0919085 | − | 0.159190i | 0 | 0 | 0 | 0.621805 | + | 1.07700i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
1745.6 | 0 | 1.31475 | − | 2.27721i | 0 | −0.934445 | + | 1.61851i | 0 | 0 | 0 | −1.95712 | − | 3.38982i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.b | odd | 2 | 1 | inner |
91.h | even | 3 | 1 | inner |
91.v | odd | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2548.2.i.m | 12 | |
7.b | odd | 2 | 1 | inner | 2548.2.i.m | 12 | |
7.c | even | 3 | 1 | 2548.2.k.g | ✓ | 12 | |
7.c | even | 3 | 1 | 2548.2.l.m | 12 | ||
7.d | odd | 6 | 1 | 2548.2.k.g | ✓ | 12 | |
7.d | odd | 6 | 1 | 2548.2.l.m | 12 | ||
13.c | even | 3 | 1 | 2548.2.l.m | 12 | ||
91.g | even | 3 | 1 | 2548.2.k.g | ✓ | 12 | |
91.h | even | 3 | 1 | inner | 2548.2.i.m | 12 | |
91.m | odd | 6 | 1 | 2548.2.k.g | ✓ | 12 | |
91.n | odd | 6 | 1 | 2548.2.l.m | 12 | ||
91.v | odd | 6 | 1 | inner | 2548.2.i.m | 12 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2548.2.i.m | 12 | 1.a | even | 1 | 1 | trivial | |
2548.2.i.m | 12 | 7.b | odd | 2 | 1 | inner | |
2548.2.i.m | 12 | 91.h | even | 3 | 1 | inner | |
2548.2.i.m | 12 | 91.v | odd | 6 | 1 | inner | |
2548.2.k.g | ✓ | 12 | 7.c | even | 3 | 1 | |
2548.2.k.g | ✓ | 12 | 7.d | odd | 6 | 1 | |
2548.2.k.g | ✓ | 12 | 91.g | even | 3 | 1 | |
2548.2.k.g | ✓ | 12 | 91.m | odd | 6 | 1 | |
2548.2.l.m | 12 | 7.c | even | 3 | 1 | ||
2548.2.l.m | 12 | 7.d | odd | 6 | 1 | ||
2548.2.l.m | 12 | 13.c | even | 3 | 1 | ||
2548.2.l.m | 12 | 91.n | odd | 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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