Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 9075.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: | 6.6.860280160.1 |
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: | no (minimal twist has level 1815) |
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 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
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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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1.1 |
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−2.42911 | −1.00000 | 3.90056 | 0 | 2.42911 | 1.34168 | −4.61665 | 1.00000 | 0 | ||||||||||||||||||||||||||||||||||||
1.2 | −1.95455 | −1.00000 | 1.82026 | 0 | 1.95455 | −2.58348 | 0.351308 | 1.00000 | 0 | |||||||||||||||||||||||||||||||||||||
1.3 | −0.0838261 | −1.00000 | −1.99297 | 0 | 0.0838261 | 2.34295 | 0.334715 | 1.00000 | 0 | |||||||||||||||||||||||||||||||||||||
1.4 | 1.19557 | −1.00000 | −0.570614 | 0 | −1.19557 | −3.76208 | −3.07335 | 1.00000 | 0 | |||||||||||||||||||||||||||||||||||||
1.5 | 1.53672 | −1.00000 | 0.361523 | 0 | −1.53672 | 2.86503 | −2.51789 | 1.00000 | 0 | |||||||||||||||||||||||||||||||||||||
1.6 | 2.73519 | −1.00000 | 5.48125 | 0 | −2.73519 | −4.20410 | 9.52186 | 1.00000 | 0 | |||||||||||||||||||||||||||||||||||||
Atkin-Lehner signs
Sign | |
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Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
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Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 9075.2.a.dr | 6 | |
5.b | even | 2 | 1 | 9075.2.a.dp | 6 | ||
5.c | odd | 4 | 2 | 1815.2.c.h | ✓ | 12 | |
11.b | odd | 2 | 1 | 9075.2.a.do | 6 | ||
55.d | odd | 2 | 1 | 9075.2.a.ds | 6 | ||
55.e | even | 4 | 2 | 1815.2.c.i | yes | 12 |
By twisted newform orbit | |||||||
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Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1815.2.c.h | ✓ | 12 | 5.c | odd | 4 | 2 | |
1815.2.c.i | yes | 12 | 55.e | even | 4 | 2 | |
9075.2.a.do | 6 | 11.b | odd | 2 | 1 | ||
9075.2.a.dp | 6 | 5.b | even | 2 | 1 | ||
9075.2.a.dr | 6 | 1.a | even | 1 | 1 | trivial | |
9075.2.a.ds | 6 | 55.d | 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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