Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6930,2,Mod(5741,6930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6930.5741");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.g (of order \(2\), degree \(1\), 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: | \(55.3363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5741.1 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.2 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.3 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.4 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.5 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.6 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.7 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.8 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.9 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.10 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.11 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.12 | −1.00000 | 0 | 1.00000 | − | 1.00000i | 0 | 1.00000i | −1.00000 | 0 | 1.00000i | |||||||||||||||||
5741.13 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.14 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.15 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.16 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.17 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.18 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.19 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
5741.20 | −1.00000 | 0 | 1.00000 | 1.00000i | 0 | − | 1.00000i | −1.00000 | 0 | − | 1.00000i | ||||||||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
33.d | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 6930.2.g.a | ✓ | 24 |
3.b | odd | 2 | 1 | 6930.2.g.d | yes | 24 | |
11.b | odd | 2 | 1 | 6930.2.g.d | yes | 24 | |
33.d | even | 2 | 1 | inner | 6930.2.g.a | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6930.2.g.a | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
6930.2.g.a | ✓ | 24 | 33.d | even | 2 | 1 | inner |
6930.2.g.d | yes | 24 | 3.b | odd | 2 | 1 | |
6930.2.g.d | yes | 24 | 11.b | odd | 2 | 1 |