Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, 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("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2925.c (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 65) |
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
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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2224.1 |
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− | 2.41421i | 0 | −3.82843 | 0 | 0 | − | 4.82843i | 4.41421i | 0 | 0 | ||||||||||||||||||||||||||||
2224.2 | − | 0.414214i | 0 | 1.82843 | 0 | 0 | − | 0.828427i | − | 1.58579i | 0 | 0 | ||||||||||||||||||||||||||||
2224.3 | 0.414214i | 0 | 1.82843 | 0 | 0 | 0.828427i | 1.58579i | 0 | 0 | |||||||||||||||||||||||||||||||
2224.4 | 2.41421i | 0 | −3.82843 | 0 | 0 | 4.82843i | − | 4.41421i | 0 | 0 | ||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
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1.a | even | 1 | 1 | trivial |
5.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 | 2925.2.c.r | 4 | |
3.b | odd | 2 | 1 | 325.2.b.f | 4 | ||
5.b | even | 2 | 1 | inner | 2925.2.c.r | 4 | |
5.c | odd | 4 | 1 | 585.2.a.m | 2 | ||
5.c | odd | 4 | 1 | 2925.2.a.u | 2 | ||
15.d | odd | 2 | 1 | 325.2.b.f | 4 | ||
15.e | even | 4 | 1 | 65.2.a.b | ✓ | 2 | |
15.e | even | 4 | 1 | 325.2.a.i | 2 | ||
20.e | even | 4 | 1 | 9360.2.a.cd | 2 | ||
60.l | odd | 4 | 1 | 1040.2.a.j | 2 | ||
60.l | odd | 4 | 1 | 5200.2.a.bu | 2 | ||
65.h | odd | 4 | 1 | 7605.2.a.x | 2 | ||
105.k | odd | 4 | 1 | 3185.2.a.j | 2 | ||
120.q | odd | 4 | 1 | 4160.2.a.z | 2 | ||
120.w | even | 4 | 1 | 4160.2.a.bf | 2 | ||
165.l | odd | 4 | 1 | 7865.2.a.j | 2 | ||
195.j | odd | 4 | 1 | 845.2.c.b | 4 | ||
195.s | even | 4 | 1 | 845.2.a.g | 2 | ||
195.s | even | 4 | 1 | 4225.2.a.r | 2 | ||
195.u | odd | 4 | 1 | 845.2.c.b | 4 | ||
195.bc | odd | 12 | 2 | 845.2.m.f | 8 | ||
195.bf | even | 12 | 2 | 845.2.e.c | 4 | ||
195.bl | even | 12 | 2 | 845.2.e.h | 4 | ||
195.bn | odd | 12 | 2 | 845.2.m.f | 8 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
65.2.a.b | ✓ | 2 | 15.e | even | 4 | 1 | |
325.2.a.i | 2 | 15.e | even | 4 | 1 | ||
325.2.b.f | 4 | 3.b | odd | 2 | 1 | ||
325.2.b.f | 4 | 15.d | odd | 2 | 1 | ||
585.2.a.m | 2 | 5.c | odd | 4 | 1 | ||
845.2.a.g | 2 | 195.s | even | 4 | 1 | ||
845.2.c.b | 4 | 195.j | odd | 4 | 1 | ||
845.2.c.b | 4 | 195.u | odd | 4 | 1 | ||
845.2.e.c | 4 | 195.bf | even | 12 | 2 | ||
845.2.e.h | 4 | 195.bl | even | 12 | 2 | ||
845.2.m.f | 8 | 195.bc | odd | 12 | 2 | ||
845.2.m.f | 8 | 195.bn | odd | 12 | 2 | ||
1040.2.a.j | 2 | 60.l | odd | 4 | 1 | ||
2925.2.a.u | 2 | 5.c | odd | 4 | 1 | ||
2925.2.c.r | 4 | 1.a | even | 1 | 1 | trivial | |
2925.2.c.r | 4 | 5.b | even | 2 | 1 | inner | |
3185.2.a.j | 2 | 105.k | odd | 4 | 1 | ||
4160.2.a.z | 2 | 120.q | odd | 4 | 1 | ||
4160.2.a.bf | 2 | 120.w | even | 4 | 1 | ||
4225.2.a.r | 2 | 195.s | even | 4 | 1 | ||
5200.2.a.bu | 2 | 60.l | odd | 4 | 1 | ||
7605.2.a.x | 2 | 65.h | odd | 4 | 1 | ||
7865.2.a.j | 2 | 165.l | odd | 4 | 1 | ||
9360.2.a.cd | 2 | 20.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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