Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
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 | −3.35325 | 1.00000 | −0.0968667 | −3.35325 | −2.67437 | 1.00000 | 8.24428 | −0.0968667 | ||||||||||||||||||
1.2 | 1.00000 | −3.11260 | 1.00000 | −0.160277 | −3.11260 | −3.29184 | 1.00000 | 6.68830 | −0.160277 | ||||||||||||||||||
1.3 | 1.00000 | −3.09514 | 1.00000 | 3.37243 | −3.09514 | 1.17193 | 1.00000 | 6.57990 | 3.37243 | ||||||||||||||||||
1.4 | 1.00000 | −2.86609 | 1.00000 | 4.19184 | −2.86609 | −2.33387 | 1.00000 | 5.21449 | 4.19184 | ||||||||||||||||||
1.5 | 1.00000 | −2.59634 | 1.00000 | −2.79905 | −2.59634 | 1.81461 | 1.00000 | 3.74100 | −2.79905 | ||||||||||||||||||
1.6 | 1.00000 | −2.58772 | 1.00000 | −1.78395 | −2.58772 | −0.188589 | 1.00000 | 3.69628 | −1.78395 | ||||||||||||||||||
1.7 | 1.00000 | −2.51773 | 1.00000 | 3.18361 | −2.51773 | 3.34442 | 1.00000 | 3.33897 | 3.18361 | ||||||||||||||||||
1.8 | 1.00000 | −2.49412 | 1.00000 | 2.01405 | −2.49412 | 2.26153 | 1.00000 | 3.22062 | 2.01405 | ||||||||||||||||||
1.9 | 1.00000 | −2.36933 | 1.00000 | −2.34107 | −2.36933 | 4.14004 | 1.00000 | 2.61374 | −2.34107 | ||||||||||||||||||
1.10 | 1.00000 | −1.89942 | 1.00000 | 0.311705 | −1.89942 | 2.23532 | 1.00000 | 0.607790 | 0.311705 | ||||||||||||||||||
1.11 | 1.00000 | −1.57271 | 1.00000 | −1.60703 | −1.57271 | −4.83422 | 1.00000 | −0.526597 | −1.60703 | ||||||||||||||||||
1.12 | 1.00000 | −1.53830 | 1.00000 | 3.94371 | −1.53830 | −3.54174 | 1.00000 | −0.633629 | 3.94371 | ||||||||||||||||||
1.13 | 1.00000 | −1.50477 | 1.00000 | 2.73541 | −1.50477 | −4.93109 | 1.00000 | −0.735674 | 2.73541 | ||||||||||||||||||
1.14 | 1.00000 | −1.45785 | 1.00000 | 0.272726 | −1.45785 | 4.58744 | 1.00000 | −0.874665 | 0.272726 | ||||||||||||||||||
1.15 | 1.00000 | −1.22639 | 1.00000 | −1.99280 | −1.22639 | −0.468701 | 1.00000 | −1.49597 | −1.99280 | ||||||||||||||||||
1.16 | 1.00000 | −1.04358 | 1.00000 | 1.25349 | −1.04358 | 0.828851 | 1.00000 | −1.91094 | 1.25349 | ||||||||||||||||||
1.17 | 1.00000 | −0.909483 | 1.00000 | 3.81385 | −0.909483 | 4.56339 | 1.00000 | −2.17284 | 3.81385 | ||||||||||||||||||
1.18 | 1.00000 | −0.905567 | 1.00000 | −1.11072 | −0.905567 | −1.83235 | 1.00000 | −2.17995 | −1.11072 | ||||||||||||||||||
1.19 | 1.00000 | −0.570351 | 1.00000 | −1.34990 | −0.570351 | −5.21632 | 1.00000 | −2.67470 | −1.34990 | ||||||||||||||||||
1.20 | 1.00000 | −0.550547 | 1.00000 | 0.337407 | −0.550547 | 1.25225 | 1.00000 | −2.69690 | 0.337407 | ||||||||||||||||||
See all 52 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(2017\) | \(1\) |
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 | 4034.2.a.d | ✓ | 52 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4034.2.a.d | ✓ | 52 | 1.a | even | 1 | 1 | trivial |