Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1224,1,Mod(11,1224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1224, base_ring=CyclotomicField(48))
chi = DirichletCharacter(H, H._module([24, 24, 8, 21]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1224.11");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1224.cx (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: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Projective image: | |
Projective field: | Galois closure of |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
The -expansion and trace form are shown below.
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
11.1 |
|
−0.608761 | − | 0.793353i | 0.793353 | − | 0.608761i | −0.258819 | + | 0.965926i | 0 | −0.965926 | − | 0.258819i | 0 | 0.923880 | − | 0.382683i | 0.258819 | − | 0.965926i | 0 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
131.1 | 0.793353 | + | 0.608761i | 0.608761 | − | 0.793353i | 0.258819 | + | 0.965926i | 0 | 0.965926 | − | 0.258819i | 0 | −0.382683 | + | 0.923880i | −0.258819 | − | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
227.1 | 0.608761 | + | 0.793353i | −0.793353 | + | 0.608761i | −0.258819 | + | 0.965926i | 0 | −0.965926 | − | 0.258819i | 0 | −0.923880 | + | 0.382683i | 0.258819 | − | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
275.1 | 0.608761 | − | 0.793353i | −0.793353 | − | 0.608761i | −0.258819 | − | 0.965926i | 0 | −0.965926 | + | 0.258819i | 0 | −0.923880 | − | 0.382683i | 0.258819 | + | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
299.1 | 0.793353 | − | 0.608761i | 0.608761 | + | 0.793353i | 0.258819 | − | 0.965926i | 0 | 0.965926 | + | 0.258819i | 0 | −0.382683 | − | 0.923880i | −0.258819 | + | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
347.1 | −0.130526 | − | 0.991445i | 0.991445 | − | 0.130526i | −0.965926 | + | 0.258819i | 0 | −0.258819 | − | 0.965926i | 0 | 0.382683 | + | 0.923880i | 0.965926 | − | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
371.1 | 0.991445 | + | 0.130526i | 0.130526 | − | 0.991445i | 0.965926 | + | 0.258819i | 0 | 0.258819 | − | 0.965926i | 0 | 0.923880 | + | 0.382683i | −0.965926 | − | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
419.1 | 0.991445 | − | 0.130526i | 0.130526 | + | 0.991445i | 0.965926 | − | 0.258819i | 0 | 0.258819 | + | 0.965926i | 0 | 0.923880 | − | 0.382683i | −0.965926 | + | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
515.1 | −0.130526 | + | 0.991445i | 0.991445 | + | 0.130526i | −0.965926 | − | 0.258819i | 0 | −0.258819 | + | 0.965926i | 0 | 0.382683 | − | 0.923880i | 0.965926 | + | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
635.1 | −0.991445 | + | 0.130526i | −0.130526 | − | 0.991445i | 0.965926 | − | 0.258819i | 0 | 0.258819 | + | 0.965926i | 0 | −0.923880 | + | 0.382683i | −0.965926 | + | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
707.1 | 0.130526 | + | 0.991445i | −0.991445 | + | 0.130526i | −0.965926 | + | 0.258819i | 0 | −0.258819 | − | 0.965926i | 0 | −0.382683 | − | 0.923880i | 0.965926 | − | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
779.1 | −0.608761 | + | 0.793353i | 0.793353 | + | 0.608761i | −0.258819 | − | 0.965926i | 0 | −0.965926 | + | 0.258819i | 0 | 0.923880 | + | 0.382683i | 0.258819 | + | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
923.1 | −0.793353 | − | 0.608761i | −0.608761 | + | 0.793353i | 0.258819 | + | 0.965926i | 0 | 0.965926 | − | 0.258819i | 0 | 0.382683 | − | 0.923880i | −0.258819 | − | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
947.1 | 0.130526 | − | 0.991445i | −0.991445 | − | 0.130526i | −0.965926 | − | 0.258819i | 0 | −0.258819 | + | 0.965926i | 0 | −0.382683 | + | 0.923880i | 0.965926 | + | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1091.1 | −0.991445 | − | 0.130526i | −0.130526 | + | 0.991445i | 0.965926 | + | 0.258819i | 0 | 0.258819 | − | 0.965926i | 0 | −0.923880 | − | 0.382683i | −0.965926 | − | 0.258819i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1163.1 | −0.793353 | + | 0.608761i | −0.608761 | − | 0.793353i | 0.258819 | − | 0.965926i | 0 | 0.965926 | + | 0.258819i | 0 | 0.382683 | + | 0.923880i | −0.258819 | + | 0.965926i | 0 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
8.d | odd | 2 | 1 | CM by |
153.s | even | 48 | 1 | inner |
1224.cx | odd | 48 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1224.1.cx.b | yes | 16 |
3.b | odd | 2 | 1 | 3672.1.dv.b | 16 | ||
8.d | odd | 2 | 1 | CM | 1224.1.cx.b | yes | 16 |
9.c | even | 3 | 1 | 3672.1.dv.a | 16 | ||
9.d | odd | 6 | 1 | 1224.1.cx.a | ✓ | 16 | |
17.e | odd | 16 | 1 | 1224.1.cx.a | ✓ | 16 | |
24.f | even | 2 | 1 | 3672.1.dv.b | 16 | ||
51.i | even | 16 | 1 | 3672.1.dv.a | 16 | ||
72.l | even | 6 | 1 | 1224.1.cx.a | ✓ | 16 | |
72.p | odd | 6 | 1 | 3672.1.dv.a | 16 | ||
136.s | even | 16 | 1 | 1224.1.cx.a | ✓ | 16 | |
153.s | even | 48 | 1 | inner | 1224.1.cx.b | yes | 16 |
153.t | odd | 48 | 1 | 3672.1.dv.b | 16 | ||
408.bg | odd | 16 | 1 | 3672.1.dv.a | 16 | ||
1224.cx | odd | 48 | 1 | inner | 1224.1.cx.b | yes | 16 |
1224.da | even | 48 | 1 | 3672.1.dv.b | 16 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1224.1.cx.a | ✓ | 16 | 9.d | odd | 6 | 1 | |
1224.1.cx.a | ✓ | 16 | 17.e | odd | 16 | 1 | |
1224.1.cx.a | ✓ | 16 | 72.l | even | 6 | 1 | |
1224.1.cx.a | ✓ | 16 | 136.s | even | 16 | 1 | |
1224.1.cx.b | yes | 16 | 1.a | even | 1 | 1 | trivial |
1224.1.cx.b | yes | 16 | 8.d | odd | 2 | 1 | CM |
1224.1.cx.b | yes | 16 | 153.s | even | 48 | 1 | inner |
1224.1.cx.b | yes | 16 | 1224.cx | odd | 48 | 1 | inner |
3672.1.dv.a | 16 | 9.c | even | 3 | 1 | ||
3672.1.dv.a | 16 | 51.i | even | 16 | 1 | ||
3672.1.dv.a | 16 | 72.p | odd | 6 | 1 | ||
3672.1.dv.a | 16 | 408.bg | odd | 16 | 1 | ||
3672.1.dv.b | 16 | 3.b | odd | 2 | 1 | ||
3672.1.dv.b | 16 | 24.f | even | 2 | 1 | ||
3672.1.dv.b | 16 | 153.t | odd | 48 | 1 | ||
3672.1.dv.b | 16 | 1224.da | even | 48 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .