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: | \(1\) |
Dimension: | \(33\) |
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 | −3.41599 | 1.00000 | 1.09379 | −3.41599 | 4.04655 | 1.00000 | 8.66901 | 1.09379 | ||||||||||||||||||
1.2 | 1.00000 | −3.31212 | 1.00000 | −3.97668 | −3.31212 | 0.855437 | 1.00000 | 7.97011 | −3.97668 | ||||||||||||||||||
1.3 | 1.00000 | −2.82298 | 1.00000 | 0.779916 | −2.82298 | −3.19115 | 1.00000 | 4.96923 | 0.779916 | ||||||||||||||||||
1.4 | 1.00000 | −2.73960 | 1.00000 | −3.73363 | −2.73960 | −3.98248 | 1.00000 | 4.50543 | −3.73363 | ||||||||||||||||||
1.5 | 1.00000 | −2.69679 | 1.00000 | −2.92996 | −2.69679 | 3.32033 | 1.00000 | 4.27265 | −2.92996 | ||||||||||||||||||
1.6 | 1.00000 | −2.68746 | 1.00000 | 1.22075 | −2.68746 | −1.79428 | 1.00000 | 4.22244 | 1.22075 | ||||||||||||||||||
1.7 | 1.00000 | −2.63161 | 1.00000 | 1.62454 | −2.63161 | 2.40683 | 1.00000 | 3.92538 | 1.62454 | ||||||||||||||||||
1.8 | 1.00000 | −2.03082 | 1.00000 | −0.733478 | −2.03082 | −1.85114 | 1.00000 | 1.12424 | −0.733478 | ||||||||||||||||||
1.9 | 1.00000 | −1.80963 | 1.00000 | 0.856694 | −1.80963 | 0.353536 | 1.00000 | 0.274766 | 0.856694 | ||||||||||||||||||
1.10 | 1.00000 | −1.73259 | 1.00000 | 3.77683 | −1.73259 | 0.621551 | 1.00000 | 0.00185264 | 3.77683 | ||||||||||||||||||
1.11 | 1.00000 | −1.72838 | 1.00000 | −2.88558 | −1.72838 | −0.799535 | 1.00000 | −0.0126910 | −2.88558 | ||||||||||||||||||
1.12 | 1.00000 | −1.65119 | 1.00000 | −2.90851 | −1.65119 | 0.175106 | 1.00000 | −0.273565 | −2.90851 | ||||||||||||||||||
1.13 | 1.00000 | −1.42842 | 1.00000 | 2.01766 | −1.42842 | 0.289927 | 1.00000 | −0.959611 | 2.01766 | ||||||||||||||||||
1.14 | 1.00000 | −0.945997 | 1.00000 | −2.44770 | −0.945997 | 2.03235 | 1.00000 | −2.10509 | −2.44770 | ||||||||||||||||||
1.15 | 1.00000 | −0.523973 | 1.00000 | 1.37573 | −0.523973 | −3.92552 | 1.00000 | −2.72545 | 1.37573 | ||||||||||||||||||
1.16 | 1.00000 | −0.423572 | 1.00000 | −0.487122 | −0.423572 | 2.40385 | 1.00000 | −2.82059 | −0.487122 | ||||||||||||||||||
1.17 | 1.00000 | −0.366256 | 1.00000 | 0.145528 | −0.366256 | 3.13381 | 1.00000 | −2.86586 | 0.145528 | ||||||||||||||||||
1.18 | 1.00000 | −0.289410 | 1.00000 | −3.81688 | −0.289410 | −2.88122 | 1.00000 | −2.91624 | −3.81688 | ||||||||||||||||||
1.19 | 1.00000 | −0.264302 | 1.00000 | 2.82441 | −0.264302 | −2.96778 | 1.00000 | −2.93014 | 2.82441 | ||||||||||||||||||
1.20 | 1.00000 | −0.138152 | 1.00000 | −3.80380 | −0.138152 | 3.68849 | 1.00000 | −2.98091 | −3.80380 | ||||||||||||||||||
See all 33 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.a | ✓ | 33 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4034.2.a.a | ✓ | 33 | 1.a | even | 1 | 1 | trivial |