Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1241,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 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("8280.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.p (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: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1241.1 | 0 | 0 | 0 | −1.00000 | 0 | − | 4.92948i | 0 | 0 | 0 | |||||||||||||||||
1241.2 | 0 | 0 | 0 | −1.00000 | 0 | − | 4.64793i | 0 | 0 | 0 | |||||||||||||||||
1241.3 | 0 | 0 | 0 | −1.00000 | 0 | − | 4.29385i | 0 | 0 | 0 | |||||||||||||||||
1241.4 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.83098i | 0 | 0 | 0 | |||||||||||||||||
1241.5 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.49780i | 0 | 0 | 0 | |||||||||||||||||
1241.6 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.21237i | 0 | 0 | 0 | |||||||||||||||||
1241.7 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.18371i | 0 | 0 | 0 | |||||||||||||||||
1241.8 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.13239i | 0 | 0 | 0 | |||||||||||||||||
1241.9 | 0 | 0 | 0 | −1.00000 | 0 | − | 3.11398i | 0 | 0 | 0 | |||||||||||||||||
1241.10 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.84853i | 0 | 0 | 0 | |||||||||||||||||
1241.11 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.78247i | 0 | 0 | 0 | |||||||||||||||||
1241.12 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.72943i | 0 | 0 | 0 | |||||||||||||||||
1241.13 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.53343i | 0 | 0 | 0 | |||||||||||||||||
1241.14 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.35143i | 0 | 0 | 0 | |||||||||||||||||
1241.15 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.09276i | 0 | 0 | 0 | |||||||||||||||||
1241.16 | 0 | 0 | 0 | −1.00000 | 0 | − | 2.08780i | 0 | 0 | 0 | |||||||||||||||||
1241.17 | 0 | 0 | 0 | −1.00000 | 0 | − | 1.46186i | 0 | 0 | 0 | |||||||||||||||||
1241.18 | 0 | 0 | 0 | −1.00000 | 0 | − | 1.44649i | 0 | 0 | 0 | |||||||||||||||||
1241.19 | 0 | 0 | 0 | −1.00000 | 0 | − | 1.36101i | 0 | 0 | 0 | |||||||||||||||||
1241.20 | 0 | 0 | 0 | −1.00000 | 0 | − | 1.20278i | 0 | 0 | 0 | |||||||||||||||||
See all 48 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
69.c | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 8280.2.p.a | ✓ | 48 |
3.b | odd | 2 | 1 | 8280.2.p.b | yes | 48 | |
23.b | odd | 2 | 1 | 8280.2.p.b | yes | 48 | |
69.c | even | 2 | 1 | inner | 8280.2.p.a | ✓ | 48 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8280.2.p.a | ✓ | 48 | 1.a | even | 1 | 1 | trivial |
8280.2.p.a | ✓ | 48 | 69.c | even | 2 | 1 | inner |
8280.2.p.b | yes | 48 | 3.b | odd | 2 | 1 | |
8280.2.p.b | yes | 48 | 23.b | odd | 2 | 1 |