Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 825.n (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: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | 8.0.819390625.1 |
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: | yes |
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
301.1 |
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−0.755243 | − | 0.548716i | 0.309017 | − | 0.951057i | −0.348732 | − | 1.07329i | 0 | −0.755243 | + | 0.548716i | −1.37328 | − | 4.22651i | −0.902506 | + | 2.77763i | −0.809017 | − | 0.587785i | 0 | ||||||||||||||||||||||||||||
301.2 | 2.06426 | + | 1.49977i | 0.309017 | − | 0.951057i | 1.39382 | + | 4.28973i | 0 | 2.06426 | − | 1.49977i | 1.44623 | + | 4.45102i | −1.97946 | + | 6.09215i | −0.809017 | − | 0.587785i | 0 | |||||||||||||||||||||||||||||
526.1 | −0.575405 | + | 1.77091i | −0.809017 | + | 0.587785i | −1.18701 | − | 0.862413i | 0 | −0.575405 | − | 1.77091i | 1.04263 | + | 0.757515i | −0.802588 | + | 0.583114i | 0.309017 | − | 0.951057i | 0 | |||||||||||||||||||||||||||||
526.2 | 0.766388 | − | 2.35870i | −0.809017 | + | 0.587785i | −3.35808 | − | 2.43978i | 0 | 0.766388 | + | 2.35870i | 2.38442 | + | 1.73238i | −4.31545 | + | 3.13535i | 0.309017 | − | 0.951057i | 0 | |||||||||||||||||||||||||||||
676.1 | −0.575405 | − | 1.77091i | −0.809017 | − | 0.587785i | −1.18701 | + | 0.862413i | 0 | −0.575405 | + | 1.77091i | 1.04263 | − | 0.757515i | −0.802588 | − | 0.583114i | 0.309017 | + | 0.951057i | 0 | |||||||||||||||||||||||||||||
676.2 | 0.766388 | + | 2.35870i | −0.809017 | − | 0.587785i | −3.35808 | + | 2.43978i | 0 | 0.766388 | − | 2.35870i | 2.38442 | − | 1.73238i | −4.31545 | − | 3.13535i | 0.309017 | + | 0.951057i | 0 | |||||||||||||||||||||||||||||
751.1 | −0.755243 | + | 0.548716i | 0.309017 | + | 0.951057i | −0.348732 | + | 1.07329i | 0 | −0.755243 | − | 0.548716i | −1.37328 | + | 4.22651i | −0.902506 | − | 2.77763i | −0.809017 | + | 0.587785i | 0 | |||||||||||||||||||||||||||||
751.2 | 2.06426 | − | 1.49977i | 0.309017 | + | 0.951057i | 1.39382 | − | 4.28973i | 0 | 2.06426 | + | 1.49977i | 1.44623 | − | 4.45102i | −1.97946 | − | 6.09215i | −0.809017 | + | 0.587785i | 0 | |||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
11.c | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 825.2.n.l | yes | 8 |
5.b | even | 2 | 1 | 825.2.n.h | ✓ | 8 | |
5.c | odd | 4 | 2 | 825.2.bx.i | 16 | ||
11.c | even | 5 | 1 | inner | 825.2.n.l | yes | 8 |
11.c | even | 5 | 1 | 9075.2.a.cp | 4 | ||
11.d | odd | 10 | 1 | 9075.2.a.dh | 4 | ||
55.h | odd | 10 | 1 | 9075.2.a.cn | 4 | ||
55.j | even | 10 | 1 | 825.2.n.h | ✓ | 8 | |
55.j | even | 10 | 1 | 9075.2.a.de | 4 | ||
55.k | odd | 20 | 2 | 825.2.bx.i | 16 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
825.2.n.h | ✓ | 8 | 5.b | even | 2 | 1 | |
825.2.n.h | ✓ | 8 | 55.j | even | 10 | 1 | |
825.2.n.l | yes | 8 | 1.a | even | 1 | 1 | trivial |
825.2.n.l | yes | 8 | 11.c | even | 5 | 1 | inner |
825.2.bx.i | 16 | 5.c | odd | 4 | 2 | ||
825.2.bx.i | 16 | 55.k | odd | 20 | 2 | ||
9075.2.a.cn | 4 | 55.h | odd | 10 | 1 | ||
9075.2.a.cp | 4 | 11.c | even | 5 | 1 | ||
9075.2.a.de | 4 | 55.j | even | 10 | 1 | ||
9075.2.a.dh | 4 | 11.d | odd | 10 | 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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