Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3022,2,Mod(1,3022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3022 = 2 \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3022.a (trivial) |
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: | yes |
Analytic conductor: | \(24.1307914908\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −1.00000 | −3.25131 | 1.00000 | 1.67924 | 3.25131 | 0.771230 | −1.00000 | 7.57100 | −1.67924 | ||||||||||||||||||
1.2 | −1.00000 | −3.07488 | 1.00000 | −0.757070 | 3.07488 | 4.15067 | −1.00000 | 6.45490 | 0.757070 | ||||||||||||||||||
1.3 | −1.00000 | −2.61479 | 1.00000 | −2.96938 | 2.61479 | −2.32994 | −1.00000 | 3.83715 | 2.96938 | ||||||||||||||||||
1.4 | −1.00000 | −2.51661 | 1.00000 | −2.42793 | 2.51661 | −4.63792 | −1.00000 | 3.33330 | 2.42793 | ||||||||||||||||||
1.5 | −1.00000 | −2.18909 | 1.00000 | 1.84095 | 2.18909 | −3.48721 | −1.00000 | 1.79209 | −1.84095 | ||||||||||||||||||
1.6 | −1.00000 | −1.86039 | 1.00000 | −3.07424 | 1.86039 | 3.10390 | −1.00000 | 0.461044 | 3.07424 | ||||||||||||||||||
1.7 | −1.00000 | −1.79666 | 1.00000 | 0.0122542 | 1.79666 | 1.12738 | −1.00000 | 0.227973 | −0.0122542 | ||||||||||||||||||
1.8 | −1.00000 | −1.67450 | 1.00000 | 0.351164 | 1.67450 | 1.57105 | −1.00000 | −0.196055 | −0.351164 | ||||||||||||||||||
1.9 | −1.00000 | −1.44839 | 1.00000 | 3.65193 | 1.44839 | −0.862475 | −1.00000 | −0.902174 | −3.65193 | ||||||||||||||||||
1.10 | −1.00000 | −1.25635 | 1.00000 | 1.44020 | 1.25635 | −1.35300 | −1.00000 | −1.42157 | −1.44020 | ||||||||||||||||||
1.11 | −1.00000 | −1.10005 | 1.00000 | 3.64757 | 1.10005 | 1.32570 | −1.00000 | −1.78989 | −3.64757 | ||||||||||||||||||
1.12 | −1.00000 | −0.918831 | 1.00000 | −3.71055 | 0.918831 | −1.09830 | −1.00000 | −2.15575 | 3.71055 | ||||||||||||||||||
1.13 | −1.00000 | −0.568978 | 1.00000 | −0.721351 | 0.568978 | −3.45953 | −1.00000 | −2.67626 | 0.721351 | ||||||||||||||||||
1.14 | −1.00000 | −0.292559 | 1.00000 | 0.592632 | 0.292559 | 3.71172 | −1.00000 | −2.91441 | −0.592632 | ||||||||||||||||||
1.15 | −1.00000 | 0.00694427 | 1.00000 | −0.256386 | −0.00694427 | 4.25103 | −1.00000 | −2.99995 | 0.256386 | ||||||||||||||||||
1.16 | −1.00000 | 0.149447 | 1.00000 | −4.01178 | −0.149447 | 1.81949 | −1.00000 | −2.97767 | 4.01178 | ||||||||||||||||||
1.17 | −1.00000 | 0.315363 | 1.00000 | 2.42301 | −0.315363 | −2.20959 | −1.00000 | −2.90055 | −2.42301 | ||||||||||||||||||
1.18 | −1.00000 | 0.856913 | 1.00000 | −1.60910 | −0.856913 | −2.98728 | −1.00000 | −2.26570 | 1.60910 | ||||||||||||||||||
1.19 | −1.00000 | 1.06292 | 1.00000 | 2.03226 | −1.06292 | 1.97033 | −1.00000 | −1.87020 | −2.03226 | ||||||||||||||||||
1.20 | −1.00000 | 1.31403 | 1.00000 | −3.53492 | −1.31403 | 1.74504 | −1.00000 | −1.27331 | 3.53492 | ||||||||||||||||||
See all 28 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(1511\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 3022.2.a.a | ✓ | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
3022.2.a.a | ✓ | 28 | 1.a | even | 1 | 1 | trivial |