Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.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: | \(64.1118877829\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
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 | −2.74790 | −2.77023 | 5.55096 | 2.51263 | 7.61233 | −1.00000 | −9.75769 | 4.67419 | −6.90446 | ||||||||||||||||||
1.2 | −2.72439 | 2.93581 | 5.42232 | 2.30642 | −7.99829 | −1.00000 | −9.32374 | 5.61896 | −6.28359 | ||||||||||||||||||
1.3 | −2.63384 | −0.440743 | 4.93710 | −2.30591 | 1.16085 | −1.00000 | −7.73583 | −2.80575 | 6.07340 | ||||||||||||||||||
1.4 | −2.57794 | −0.202180 | 4.64578 | 0.528676 | 0.521207 | −1.00000 | −6.82066 | −2.95912 | −1.36290 | ||||||||||||||||||
1.5 | −2.53036 | 1.19896 | 4.40274 | 2.21645 | −3.03381 | −1.00000 | −6.07981 | −1.56249 | −5.60842 | ||||||||||||||||||
1.6 | −2.41746 | −2.90923 | 3.84410 | −3.42697 | 7.03294 | −1.00000 | −4.45803 | 5.46362 | 8.28456 | ||||||||||||||||||
1.7 | −2.31869 | −1.99799 | 3.37631 | −0.655219 | 4.63272 | −1.00000 | −3.19123 | 0.991981 | 1.51925 | ||||||||||||||||||
1.8 | −2.27937 | −0.146043 | 3.19554 | −4.14410 | 0.332887 | −1.00000 | −2.72508 | −2.97867 | 9.44595 | ||||||||||||||||||
1.9 | −2.21183 | 1.21496 | 2.89218 | −1.78899 | −2.68729 | −1.00000 | −1.97335 | −1.52387 | 3.95694 | ||||||||||||||||||
1.10 | −2.20302 | 0.911547 | 2.85328 | 3.20458 | −2.00815 | −1.00000 | −1.87979 | −2.16908 | −7.05973 | ||||||||||||||||||
1.11 | −2.04116 | 1.10763 | 2.16635 | −1.94120 | −2.26085 | −1.00000 | −0.339541 | −1.77316 | 3.96231 | ||||||||||||||||||
1.12 | −1.95297 | −1.58711 | 1.81410 | 3.53259 | 3.09958 | −1.00000 | 0.363050 | −0.481092 | −6.89905 | ||||||||||||||||||
1.13 | −1.93505 | 2.52265 | 1.74443 | −2.95034 | −4.88147 | −1.00000 | 0.494535 | 3.36378 | 5.70906 | ||||||||||||||||||
1.14 | −1.79821 | 0.748872 | 1.23355 | 0.832366 | −1.34663 | −1.00000 | 1.37824 | −2.43919 | −1.49676 | ||||||||||||||||||
1.15 | −1.75548 | −2.49596 | 1.08173 | −0.0382408 | 4.38163 | −1.00000 | 1.61202 | 3.22983 | 0.0671311 | ||||||||||||||||||
1.16 | −1.70146 | 3.23997 | 0.894957 | −1.00710 | −5.51266 | −1.00000 | 1.88018 | 7.49737 | 1.71354 | ||||||||||||||||||
1.17 | −1.63063 | −2.88443 | 0.658946 | 1.48735 | 4.70344 | −1.00000 | 2.18676 | 5.31995 | −2.42532 | ||||||||||||||||||
1.18 | −1.61963 | 0.534433 | 0.623195 | 3.20836 | −0.865582 | −1.00000 | 2.22991 | −2.71438 | −5.19635 | ||||||||||||||||||
1.19 | −1.30150 | −1.62706 | −0.306090 | 1.44263 | 2.11762 | −1.00000 | 3.00138 | −0.352687 | −1.87759 | ||||||||||||||||||
1.20 | −1.11933 | 2.01365 | −0.747091 | −3.36606 | −2.25395 | −1.00000 | 3.07491 | 1.05478 | 3.76774 | ||||||||||||||||||
See all 69 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(7\) | \(1\) |
\(31\) | \(-1\) |
\(37\) | \(1\) |
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 | 8029.2.a.e | ✓ | 69 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8029.2.a.e | ✓ | 69 | 1.a | even | 1 | 1 | trivial |