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: | \(49\) |
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 | −3.15201 | 1.00000 | −2.19549 | 3.15201 | −1.72689 | −1.00000 | 6.93518 | 2.19549 | ||||||||||||||||||
1.2 | −1.00000 | −3.09927 | 1.00000 | −2.61970 | 3.09927 | −2.12795 | −1.00000 | 6.60550 | 2.61970 | ||||||||||||||||||
1.3 | −1.00000 | −2.82194 | 1.00000 | −1.46398 | 2.82194 | 3.02991 | −1.00000 | 4.96334 | 1.46398 | ||||||||||||||||||
1.4 | −1.00000 | −2.80221 | 1.00000 | 1.91358 | 2.80221 | −1.55673 | −1.00000 | 4.85238 | −1.91358 | ||||||||||||||||||
1.5 | −1.00000 | −2.75660 | 1.00000 | 3.24124 | 2.75660 | 3.57367 | −1.00000 | 4.59882 | −3.24124 | ||||||||||||||||||
1.6 | −1.00000 | −2.73587 | 1.00000 | −3.97663 | 2.73587 | 4.88134 | −1.00000 | 4.48496 | 3.97663 | ||||||||||||||||||
1.7 | −1.00000 | −2.70268 | 1.00000 | 1.64140 | 2.70268 | 4.14098 | −1.00000 | 4.30446 | −1.64140 | ||||||||||||||||||
1.8 | −1.00000 | −2.62176 | 1.00000 | 1.44534 | 2.62176 | −4.09354 | −1.00000 | 3.87363 | −1.44534 | ||||||||||||||||||
1.9 | −1.00000 | −2.38186 | 1.00000 | 1.49052 | 2.38186 | −1.41584 | −1.00000 | 2.67326 | −1.49052 | ||||||||||||||||||
1.10 | −1.00000 | −1.96102 | 1.00000 | 1.55397 | 1.96102 | −2.12307 | −1.00000 | 0.845608 | −1.55397 | ||||||||||||||||||
1.11 | −1.00000 | −1.82471 | 1.00000 | −3.41474 | 1.82471 | −0.804060 | −1.00000 | 0.329557 | 3.41474 | ||||||||||||||||||
1.12 | −1.00000 | −1.80649 | 1.00000 | 0.991336 | 1.80649 | 3.46798 | −1.00000 | 0.263400 | −0.991336 | ||||||||||||||||||
1.13 | −1.00000 | −1.65034 | 1.00000 | −3.69499 | 1.65034 | 0.484734 | −1.00000 | −0.276387 | 3.69499 | ||||||||||||||||||
1.14 | −1.00000 | −1.64240 | 1.00000 | −1.67247 | 1.64240 | −0.216059 | −1.00000 | −0.302515 | 1.67247 | ||||||||||||||||||
1.15 | −1.00000 | −1.33333 | 1.00000 | 2.98893 | 1.33333 | 1.91777 | −1.00000 | −1.22223 | −2.98893 | ||||||||||||||||||
1.16 | −1.00000 | −1.09618 | 1.00000 | −0.358556 | 1.09618 | −2.93033 | −1.00000 | −1.79840 | 0.358556 | ||||||||||||||||||
1.17 | −1.00000 | −0.796272 | 1.00000 | −4.15767 | 0.796272 | 2.72658 | −1.00000 | −2.36595 | 4.15767 | ||||||||||||||||||
1.18 | −1.00000 | −0.604236 | 1.00000 | −1.43680 | 0.604236 | 3.64541 | −1.00000 | −2.63490 | 1.43680 | ||||||||||||||||||
1.19 | −1.00000 | −0.600384 | 1.00000 | 0.151444 | 0.600384 | −2.68719 | −1.00000 | −2.63954 | −0.151444 | ||||||||||||||||||
1.20 | −1.00000 | −0.372757 | 1.00000 | 0.124605 | 0.372757 | −2.88406 | −1.00000 | −2.86105 | −0.124605 | ||||||||||||||||||
See all 49 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.c | ✓ | 49 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4034.2.a.c | ✓ | 49 | 1.a | even | 1 | 1 | trivial |