Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(589,2548)]
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, 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("2548.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2548.u (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: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
589.1 |
|
0 | −1.55551 | + | 2.69422i | 0 | 1.19594i | 0 | 0 | 0 | −3.33921 | − | 5.78368i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.2 | 0 | −1.19055 | + | 2.06209i | 0 | − | 1.91620i | 0 | 0 | 0 | −1.33482 | − | 2.31198i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.3 | 0 | −0.893365 | + | 1.54735i | 0 | 1.41239i | 0 | 0 | 0 | −0.0962010 | − | 0.166625i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.4 | 0 | −0.141496 | + | 0.245078i | 0 | − | 0.818894i | 0 | 0 | 0 | 1.45996 | + | 2.52872i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.5 | 0 | −0.118765 | + | 0.205706i | 0 | − | 2.57768i | 0 | 0 | 0 | 1.47179 | + | 2.54921i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.6 | 0 | 0.302937 | − | 0.524702i | 0 | 4.02670i | 0 | 0 | 0 | 1.31646 | + | 2.28017i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.7 | 0 | 0.591009 | − | 1.02366i | 0 | − | 3.88123i | 0 | 0 | 0 | 0.801416 | + | 1.38809i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.8 | 0 | 1.23985 | − | 2.14749i | 0 | 0.559885i | 0 | 0 | 0 | −1.57447 | − | 2.72707i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
589.9 | 0 | 1.26588 | − | 2.19257i | 0 | 1.99909i | 0 | 0 | 0 | −1.70492 | − | 2.95301i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.1 | 0 | −1.55551 | − | 2.69422i | 0 | − | 1.19594i | 0 | 0 | 0 | −3.33921 | + | 5.78368i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.2 | 0 | −1.19055 | − | 2.06209i | 0 | 1.91620i | 0 | 0 | 0 | −1.33482 | + | 2.31198i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.3 | 0 | −0.893365 | − | 1.54735i | 0 | − | 1.41239i | 0 | 0 | 0 | −0.0962010 | + | 0.166625i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.4 | 0 | −0.141496 | − | 0.245078i | 0 | 0.818894i | 0 | 0 | 0 | 1.45996 | − | 2.52872i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.5 | 0 | −0.118765 | − | 0.205706i | 0 | 2.57768i | 0 | 0 | 0 | 1.47179 | − | 2.54921i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.6 | 0 | 0.302937 | + | 0.524702i | 0 | − | 4.02670i | 0 | 0 | 0 | 1.31646 | − | 2.28017i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.7 | 0 | 0.591009 | + | 1.02366i | 0 | 3.88123i | 0 | 0 | 0 | 0.801416 | − | 1.38809i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.8 | 0 | 1.23985 | + | 2.14749i | 0 | − | 0.559885i | 0 | 0 | 0 | −1.57447 | + | 2.72707i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1765.9 | 0 | 1.26588 | + | 2.19257i | 0 | − | 1.99909i | 0 | 0 | 0 | −1.70492 | + | 2.95301i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.e | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2548.2.u.d | 18 | |
7.b | odd | 2 | 1 | 2548.2.u.e | 18 | ||
7.c | even | 3 | 1 | 2548.2.bb.f | 18 | ||
7.c | even | 3 | 1 | 2548.2.bq.f | 18 | ||
7.d | odd | 6 | 1 | 364.2.bb.a | ✓ | 18 | |
7.d | odd | 6 | 1 | 364.2.bq.a | yes | 18 | |
13.e | even | 6 | 1 | inner | 2548.2.u.d | 18 | |
21.g | even | 6 | 1 | 3276.2.fe.i | 18 | ||
21.g | even | 6 | 1 | 3276.2.hi.i | 18 | ||
91.k | even | 6 | 1 | 2548.2.bq.f | 18 | ||
91.l | odd | 6 | 1 | 364.2.bq.a | yes | 18 | |
91.p | odd | 6 | 1 | 364.2.bb.a | ✓ | 18 | |
91.t | odd | 6 | 1 | 2548.2.u.e | 18 | ||
91.u | even | 6 | 1 | 2548.2.bb.f | 18 | ||
273.y | even | 6 | 1 | 3276.2.hi.i | 18 | ||
273.br | even | 6 | 1 | 3276.2.fe.i | 18 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
364.2.bb.a | ✓ | 18 | 7.d | odd | 6 | 1 | |
364.2.bb.a | ✓ | 18 | 91.p | odd | 6 | 1 | |
364.2.bq.a | yes | 18 | 7.d | odd | 6 | 1 | |
364.2.bq.a | yes | 18 | 91.l | odd | 6 | 1 | |
2548.2.u.d | 18 | 1.a | even | 1 | 1 | trivial | |
2548.2.u.d | 18 | 13.e | even | 6 | 1 | inner | |
2548.2.u.e | 18 | 7.b | odd | 2 | 1 | ||
2548.2.u.e | 18 | 91.t | odd | 6 | 1 | ||
2548.2.bb.f | 18 | 7.c | even | 3 | 1 | ||
2548.2.bb.f | 18 | 91.u | even | 6 | 1 | ||
2548.2.bq.f | 18 | 7.c | even | 3 | 1 | ||
2548.2.bq.f | 18 | 91.k | even | 6 | 1 | ||
3276.2.fe.i | 18 | 21.g | even | 6 | 1 | ||
3276.2.fe.i | 18 | 273.br | even | 6 | 1 | ||
3276.2.hi.i | 18 | 21.g | even | 6 | 1 | ||
3276.2.hi.i | 18 | 273.y | even | 6 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .