Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1351,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1521.b (of order , degree , not 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: | |
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 39) |
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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1351.1 |
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− | 2.56155i | 0 | −4.56155 | − | 0.561553i | 0 | 3.56155i | 6.56155i | 0 | −1.43845 | ||||||||||||||||||||||||||||
1351.2 | − | 1.56155i | 0 | −0.438447 | − | 3.56155i | 0 | 0.561553i | − | 2.43845i | 0 | −5.56155 | ||||||||||||||||||||||||||||
1351.3 | 1.56155i | 0 | −0.438447 | 3.56155i | 0 | − | 0.561553i | 2.43845i | 0 | −5.56155 | ||||||||||||||||||||||||||||||
1351.4 | 2.56155i | 0 | −4.56155 | 0.561553i | 0 | − | 3.56155i | − | 6.56155i | 0 | −1.43845 | |||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
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Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1521.2.b.h | 4 | |
3.b | odd | 2 | 1 | 507.2.b.d | 4 | ||
13.b | even | 2 | 1 | inner | 1521.2.b.h | 4 | |
13.d | odd | 4 | 1 | 1521.2.a.g | 2 | ||
13.d | odd | 4 | 1 | 1521.2.a.m | 2 | ||
13.f | odd | 12 | 2 | 117.2.g.c | 4 | ||
39.d | odd | 2 | 1 | 507.2.b.d | 4 | ||
39.f | even | 4 | 1 | 507.2.a.d | 2 | ||
39.f | even | 4 | 1 | 507.2.a.g | 2 | ||
39.h | odd | 6 | 2 | 507.2.j.g | 8 | ||
39.i | odd | 6 | 2 | 507.2.j.g | 8 | ||
39.k | even | 12 | 2 | 39.2.e.b | ✓ | 4 | |
39.k | even | 12 | 2 | 507.2.e.g | 4 | ||
52.l | even | 12 | 2 | 1872.2.t.r | 4 | ||
156.l | odd | 4 | 1 | 8112.2.a.bk | 2 | ||
156.l | odd | 4 | 1 | 8112.2.a.bo | 2 | ||
156.v | odd | 12 | 2 | 624.2.q.h | 4 | ||
195.bc | odd | 12 | 2 | 975.2.bb.i | 8 | ||
195.bh | even | 12 | 2 | 975.2.i.k | 4 | ||
195.bn | odd | 12 | 2 | 975.2.bb.i | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
39.2.e.b | ✓ | 4 | 39.k | even | 12 | 2 | |
117.2.g.c | 4 | 13.f | odd | 12 | 2 | ||
507.2.a.d | 2 | 39.f | even | 4 | 1 | ||
507.2.a.g | 2 | 39.f | even | 4 | 1 | ||
507.2.b.d | 4 | 3.b | odd | 2 | 1 | ||
507.2.b.d | 4 | 39.d | odd | 2 | 1 | ||
507.2.e.g | 4 | 39.k | even | 12 | 2 | ||
507.2.j.g | 8 | 39.h | odd | 6 | 2 | ||
507.2.j.g | 8 | 39.i | odd | 6 | 2 | ||
624.2.q.h | 4 | 156.v | odd | 12 | 2 | ||
975.2.i.k | 4 | 195.bh | even | 12 | 2 | ||
975.2.bb.i | 8 | 195.bc | odd | 12 | 2 | ||
975.2.bb.i | 8 | 195.bn | odd | 12 | 2 | ||
1521.2.a.g | 2 | 13.d | odd | 4 | 1 | ||
1521.2.a.m | 2 | 13.d | odd | 4 | 1 | ||
1521.2.b.h | 4 | 1.a | even | 1 | 1 | trivial | |
1521.2.b.h | 4 | 13.b | even | 2 | 1 | inner | |
1872.2.t.r | 4 | 52.l | even | 12 | 2 | ||
8112.2.a.bk | 2 | 156.l | odd | 4 | 1 | ||
8112.2.a.bo | 2 | 156.l | odd | 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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