Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3325,2,Mod(1,3325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3325.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 3325.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
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Defining polynomial: |
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Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 665) |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
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1.1 |
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−2.66888 | −0.321744 | 5.12292 | 0 | 0.858696 | −1.00000 | −8.33471 | −2.89648 | 0 | ||||||||||||||||||||||||||||||||||||||||||
1.2 | −2.22346 | 2.66100 | 2.94379 | 0 | −5.91664 | −1.00000 | −2.09848 | 4.08093 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.3 | −1.84638 | −1.55242 | 1.40913 | 0 | 2.86637 | −1.00000 | 1.09097 | −0.589984 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.4 | −0.777584 | −2.65879 | −1.39536 | 0 | 2.06743 | −1.00000 | 2.64018 | 4.06915 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.5 | 0.0903326 | 1.28544 | −1.99184 | 0 | 0.116117 | −1.00000 | −0.360593 | −1.34766 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.6 | 0.730875 | −0.878233 | −1.46582 | 0 | −0.641878 | −1.00000 | −2.53308 | −2.22871 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.7 | 1.92614 | 3.21872 | 1.71000 | 0 | 6.19970 | −1.00000 | −0.558573 | 7.36017 | 0 | |||||||||||||||||||||||||||||||||||||||||||
1.8 | 2.76897 | 1.24603 | 5.66718 | 0 | 3.45021 | −1.00000 | 10.1543 | −1.44742 | 0 | |||||||||||||||||||||||||||||||||||||||||||
Atkin-Lehner signs
Sign | |
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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 | 3325.2.a.y | 8 | |
5.b | even | 2 | 1 | 665.2.a.k | ✓ | 8 | |
15.d | odd | 2 | 1 | 5985.2.a.bq | 8 | ||
35.c | odd | 2 | 1 | 4655.2.a.bi | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
665.2.a.k | ✓ | 8 | 5.b | even | 2 | 1 | |
3325.2.a.y | 8 | 1.a | even | 1 | 1 | trivial | |
4655.2.a.bi | 8 | 35.c | odd | 2 | 1 | ||
5985.2.a.bq | 8 | 15.d | odd | 2 | 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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