Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,1,Mod(1101,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.1101");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 3800.o (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: | 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: | yes |
Projective image: | |
Projective field: | Galois closure of 9.1.8340544000000.1 |
-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 :
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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1101.1 |
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−1.00000 | −1.53209 | 1.00000 | 0 | 1.53209 | 0.347296 | −1.00000 | 1.34730 | 0 | |||||||||||||||||||||||||||
1101.2 | −1.00000 | −0.347296 | 1.00000 | 0 | 0.347296 | −1.87939 | −1.00000 | −0.879385 | 0 | ||||||||||||||||||||||||||||
1101.3 | −1.00000 | 1.87939 | 1.00000 | 0 | −1.87939 | 1.53209 | −1.00000 | 2.53209 | 0 | ||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
152.g | odd | 2 | 1 | CM by |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 3800.1.o.c | ✓ | 3 |
5.b | even | 2 | 1 | 3800.1.o.e | yes | 3 | |
5.c | odd | 4 | 2 | 3800.1.b.d | 6 | ||
8.b | even | 2 | 1 | 3800.1.o.f | yes | 3 | |
19.b | odd | 2 | 1 | 3800.1.o.f | yes | 3 | |
40.f | even | 2 | 1 | 3800.1.o.d | yes | 3 | |
40.i | odd | 4 | 2 | 3800.1.b.c | 6 | ||
95.d | odd | 2 | 1 | 3800.1.o.d | yes | 3 | |
95.g | even | 4 | 2 | 3800.1.b.c | 6 | ||
152.g | odd | 2 | 1 | CM | 3800.1.o.c | ✓ | 3 |
760.b | odd | 2 | 1 | 3800.1.o.e | yes | 3 | |
760.t | even | 4 | 2 | 3800.1.b.d | 6 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
3800.1.b.c | 6 | 40.i | odd | 4 | 2 | ||
3800.1.b.c | 6 | 95.g | even | 4 | 2 | ||
3800.1.b.d | 6 | 5.c | odd | 4 | 2 | ||
3800.1.b.d | 6 | 760.t | even | 4 | 2 | ||
3800.1.o.c | ✓ | 3 | 1.a | even | 1 | 1 | trivial |
3800.1.o.c | ✓ | 3 | 152.g | odd | 2 | 1 | CM |
3800.1.o.d | yes | 3 | 40.f | even | 2 | 1 | |
3800.1.o.d | yes | 3 | 95.d | odd | 2 | 1 | |
3800.1.o.e | yes | 3 | 5.b | even | 2 | 1 | |
3800.1.o.e | yes | 3 | 760.b | odd | 2 | 1 | |
3800.1.o.f | yes | 3 | 8.b | even | 2 | 1 | |
3800.1.o.f | yes | 3 | 19.b | 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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