Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,10,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 175.a (trivial) |
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: | yes |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
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 35) |
Fricke sign: | |
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
:
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 | ||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 |
|
−33.3659 | 72.5961 | 601.285 | 0 | −2422.24 | 2401.00 | −2979.08 | −14412.8 | 0 | ||||||||||||||||||||||||||||||
1.2 | −15.4436 | −137.736 | −273.496 | 0 | 2127.13 | 2401.00 | 12130.9 | −711.820 | 0 | |||||||||||||||||||||||||||||||
1.3 | 25.9629 | 209.523 | 162.070 | 0 | 5439.82 | 2401.00 | −9085.18 | 24216.9 | 0 | |||||||||||||||||||||||||||||||
1.4 | 41.8466 | −126.383 | 1239.14 | 0 | −5288.71 | 2401.00 | 30428.4 | −3710.28 | 0 | |||||||||||||||||||||||||||||||
Atkin-Lehner signs
Sign | |
---|---|
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 175.10.a.e | 4 | |
5.b | even | 2 | 1 | 35.10.a.c | ✓ | 4 | |
5.c | odd | 4 | 2 | 175.10.b.e | 8 | ||
15.d | odd | 2 | 1 | 315.10.a.g | 4 | ||
35.c | odd | 2 | 1 | 245.10.a.e | 4 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
35.10.a.c | ✓ | 4 | 5.b | even | 2 | 1 | |
175.10.a.e | 4 | 1.a | even | 1 | 1 | trivial | |
175.10.b.e | 8 | 5.c | odd | 4 | 2 | ||
245.10.a.e | 4 | 35.c | odd | 2 | 1 | ||
315.10.a.g | 4 | 15.d | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .