Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 245.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 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 . We also show the integral -expansion of the trace form.
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 |
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−4.41421 | −3.24264 | 11.4853 | −5.00000 | 14.3137 | 0 | −15.3848 | −16.4853 | 22.0711 | ||||||||||||||||||||||||
1.2 | −1.58579 | 5.24264 | −5.48528 | −5.00000 | −8.31371 | 0 | 21.3848 | 0.485281 | 7.92893 | |||||||||||||||||||||||||
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 | 245.4.a.h | 2 | |
3.b | odd | 2 | 1 | 2205.4.a.bg | 2 | ||
5.b | even | 2 | 1 | 1225.4.a.v | 2 | ||
7.b | odd | 2 | 1 | 245.4.a.g | 2 | ||
7.c | even | 3 | 2 | 245.4.e.l | 4 | ||
7.d | odd | 6 | 2 | 35.4.e.b | ✓ | 4 | |
21.c | even | 2 | 1 | 2205.4.a.bf | 2 | ||
21.g | even | 6 | 2 | 315.4.j.c | 4 | ||
28.f | even | 6 | 2 | 560.4.q.i | 4 | ||
35.c | odd | 2 | 1 | 1225.4.a.x | 2 | ||
35.i | odd | 6 | 2 | 175.4.e.c | 4 | ||
35.k | even | 12 | 4 | 175.4.k.c | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
35.4.e.b | ✓ | 4 | 7.d | odd | 6 | 2 | |
175.4.e.c | 4 | 35.i | odd | 6 | 2 | ||
175.4.k.c | 8 | 35.k | even | 12 | 4 | ||
245.4.a.g | 2 | 7.b | odd | 2 | 1 | ||
245.4.a.h | 2 | 1.a | even | 1 | 1 | trivial | |
245.4.e.l | 4 | 7.c | even | 3 | 2 | ||
315.4.j.c | 4 | 21.g | even | 6 | 2 | ||
560.4.q.i | 4 | 28.f | even | 6 | 2 | ||
1225.4.a.v | 2 | 5.b | even | 2 | 1 | ||
1225.4.a.x | 2 | 35.c | odd | 2 | 1 | ||
2205.4.a.bf | 2 | 21.c | even | 2 | 1 | ||
2205.4.a.bg | 2 | 3.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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