Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [368,2,Mod(49,368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(368, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("368.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 368.m (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
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 46) |
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 primitive root of unity . We also show the integral -expansion of the trace form.
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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
49.1 |
|
0 | −0.580699 | + | 1.27155i | 0 | −1.66741 | + | 1.92429i | 0 | −1.75667 | + | 1.12894i | 0 | 0.684944 | + | 0.790468i | 0 | ||||||||||||||||||||||||||||||||||||||||
81.1 | 0 | 0.0530529 | − | 0.368991i | 0 | −3.26024 | + | 0.957293i | 0 | 0.297176 | + | 0.342959i | 0 | 2.74514 | + | 0.806046i | 0 | |||||||||||||||||||||||||||||||||||||||||
177.1 | 0 | 2.71616 | − | 1.74557i | 0 | 0.985691 | + | 2.15836i | 0 | −0.381761 | + | 0.112095i | 0 | 3.08427 | − | 6.75361i | 0 | |||||||||||||||||||||||||||||||||||||||||
193.1 | 0 | −0.712591 | − | 0.822373i | 0 | 0.174863 | + | 1.21620i | 0 | −0.260554 | + | 0.570534i | 0 | 0.258432 | − | 1.79743i | 0 | |||||||||||||||||||||||||||||||||||||||||
209.1 | 0 | 0.0530529 | + | 0.368991i | 0 | −3.26024 | − | 0.957293i | 0 | 0.297176 | − | 0.342959i | 0 | 2.74514 | − | 0.806046i | 0 | |||||||||||||||||||||||||||||||||||||||||
225.1 | 0 | −0.712591 | + | 0.822373i | 0 | 0.174863 | − | 1.21620i | 0 | −0.260554 | − | 0.570534i | 0 | 0.258432 | + | 1.79743i | 0 | |||||||||||||||||||||||||||||||||||||||||
257.1 | 0 | 0.524075 | − | 0.153882i | 0 | 0.767092 | + | 0.492980i | 0 | 0.601808 | + | 4.18567i | 0 | −2.27279 | + | 1.46063i | 0 | |||||||||||||||||||||||||||||||||||||||||
289.1 | 0 | 2.71616 | + | 1.74557i | 0 | 0.985691 | − | 2.15836i | 0 | −0.381761 | − | 0.112095i | 0 | 3.08427 | + | 6.75361i | 0 | |||||||||||||||||||||||||||||||||||||||||
305.1 | 0 | 0.524075 | + | 0.153882i | 0 | 0.767092 | − | 0.492980i | 0 | 0.601808 | − | 4.18567i | 0 | −2.27279 | − | 1.46063i | 0 | |||||||||||||||||||||||||||||||||||||||||
353.1 | 0 | −0.580699 | − | 1.27155i | 0 | −1.66741 | − | 1.92429i | 0 | −1.75667 | − | 1.12894i | 0 | 0.684944 | − | 0.790468i | 0 | |||||||||||||||||||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.c | even | 11 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 368.2.m.b | 10 | |
4.b | odd | 2 | 1 | 46.2.c.a | ✓ | 10 | |
12.b | even | 2 | 1 | 414.2.i.f | 10 | ||
23.c | even | 11 | 1 | inner | 368.2.m.b | 10 | |
23.c | even | 11 | 1 | 8464.2.a.bx | 5 | ||
23.d | odd | 22 | 1 | 8464.2.a.bw | 5 | ||
92.g | odd | 22 | 1 | 46.2.c.a | ✓ | 10 | |
92.g | odd | 22 | 1 | 1058.2.a.m | 5 | ||
92.h | even | 22 | 1 | 1058.2.a.l | 5 | ||
276.j | odd | 22 | 1 | 9522.2.a.bu | 5 | ||
276.o | even | 22 | 1 | 414.2.i.f | 10 | ||
276.o | even | 22 | 1 | 9522.2.a.bp | 5 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
46.2.c.a | ✓ | 10 | 4.b | odd | 2 | 1 | |
46.2.c.a | ✓ | 10 | 92.g | odd | 22 | 1 | |
368.2.m.b | 10 | 1.a | even | 1 | 1 | trivial | |
368.2.m.b | 10 | 23.c | even | 11 | 1 | inner | |
414.2.i.f | 10 | 12.b | even | 2 | 1 | ||
414.2.i.f | 10 | 276.o | even | 22 | 1 | ||
1058.2.a.l | 5 | 92.h | even | 22 | 1 | ||
1058.2.a.m | 5 | 92.g | odd | 22 | 1 | ||
8464.2.a.bw | 5 | 23.d | odd | 22 | 1 | ||
8464.2.a.bx | 5 | 23.c | even | 11 | 1 | ||
9522.2.a.bp | 5 | 276.o | even | 22 | 1 | ||
9522.2.a.bu | 5 | 276.j | odd | 22 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
acting on .