Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,2,Mod(349,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 435.c (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: | |
Coefficient field: | 10.0.3899266318336.1 |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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349.1 |
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− | 2.51908i | 1.00000i | −4.34577 | −1.27413 | + | 1.83755i | 2.51908 | − | 0.173311i | 5.90919i | −1.00000 | 4.62893 | + | 3.20964i | ||||||||||||||||||||||||||||||||||||||||||
349.2 | − | 2.15351i | 1.00000i | −2.63760 | −0.0286357 | − | 2.23588i | 2.15351 | − | 1.51591i | 1.37308i | −1.00000 | −4.81500 | + | 0.0616673i | |||||||||||||||||||||||||||||||||||||||||||
349.3 | − | 1.71457i | − | 1.00000i | −0.939748 | 1.51903 | + | 1.64090i | −1.71457 | − | 0.654317i | − | 1.81788i | −1.00000 | 2.81344 | − | 2.60448i | |||||||||||||||||||||||||||||||||||||||||
349.4 | − | 0.754474i | 1.00000i | 1.43077 | −2.23474 | + | 0.0770824i | 0.754474 | − | 4.18524i | − | 2.58843i | −1.00000 | 0.0581566 | + | 1.68605i | ||||||||||||||||||||||||||||||||||||||||||
349.5 | − | 0.712495i | − | 1.00000i | 1.49235 | 2.01848 | − | 0.962154i | −0.712495 | 2.77986i | − | 2.48828i | −1.00000 | −0.685530 | − | 1.43816i | ||||||||||||||||||||||||||||||||||||||||||
349.6 | 0.712495i | 1.00000i | 1.49235 | 2.01848 | + | 0.962154i | −0.712495 | − | 2.77986i | 2.48828i | −1.00000 | −0.685530 | + | 1.43816i | ||||||||||||||||||||||||||||||||||||||||||||
349.7 | 0.754474i | − | 1.00000i | 1.43077 | −2.23474 | − | 0.0770824i | 0.754474 | 4.18524i | 2.58843i | −1.00000 | 0.0581566 | − | 1.68605i | ||||||||||||||||||||||||||||||||||||||||||||
349.8 | 1.71457i | 1.00000i | −0.939748 | 1.51903 | − | 1.64090i | −1.71457 | 0.654317i | 1.81788i | −1.00000 | 2.81344 | + | 2.60448i | |||||||||||||||||||||||||||||||||||||||||||||
349.9 | 2.15351i | − | 1.00000i | −2.63760 | −0.0286357 | + | 2.23588i | 2.15351 | 1.51591i | − | 1.37308i | −1.00000 | −4.81500 | − | 0.0616673i | |||||||||||||||||||||||||||||||||||||||||||
349.10 | 2.51908i | − | 1.00000i | −4.34577 | −1.27413 | − | 1.83755i | 2.51908 | 0.173311i | − | 5.90919i | −1.00000 | 4.62893 | − | 3.20964i | |||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 435.2.c.e | ✓ | 10 |
3.b | odd | 2 | 1 | 1305.2.c.j | 10 | ||
5.b | even | 2 | 1 | inner | 435.2.c.e | ✓ | 10 |
5.c | odd | 4 | 1 | 2175.2.a.w | 5 | ||
5.c | odd | 4 | 1 | 2175.2.a.z | 5 | ||
15.d | odd | 2 | 1 | 1305.2.c.j | 10 | ||
15.e | even | 4 | 1 | 6525.2.a.bl | 5 | ||
15.e | even | 4 | 1 | 6525.2.a.bs | 5 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
435.2.c.e | ✓ | 10 | 1.a | even | 1 | 1 | trivial |
435.2.c.e | ✓ | 10 | 5.b | even | 2 | 1 | inner |
1305.2.c.j | 10 | 3.b | odd | 2 | 1 | ||
1305.2.c.j | 10 | 15.d | odd | 2 | 1 | ||
2175.2.a.w | 5 | 5.c | odd | 4 | 1 | ||
2175.2.a.z | 5 | 5.c | odd | 4 | 1 | ||
6525.2.a.bl | 5 | 15.e | even | 4 | 1 | ||
6525.2.a.bs | 5 | 15.e | even | 4 | 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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