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: | \(1\) |
Dimension: | \(66\) |
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 | −2.81175 | 2.76808 | 5.90594 | −3.53948 | −7.78315 | −1.00000 | −10.9825 | 4.66227 | 9.95212 | ||||||||||||||||||
1.2 | −2.79803 | −1.13977 | 5.82896 | −1.02467 | 3.18910 | −1.00000 | −10.7135 | −1.70093 | 2.86704 | ||||||||||||||||||
1.3 | −2.61771 | −0.689936 | 4.85243 | 2.29234 | 1.80605 | −1.00000 | −7.46685 | −2.52399 | −6.00069 | ||||||||||||||||||
1.4 | −2.61517 | −0.260032 | 4.83913 | −2.96628 | 0.680030 | −1.00000 | −7.42483 | −2.93238 | 7.75734 | ||||||||||||||||||
1.5 | −2.58221 | 2.63278 | 4.66779 | 2.83101 | −6.79837 | −1.00000 | −6.88879 | 3.93151 | −7.31025 | ||||||||||||||||||
1.6 | −2.40369 | −3.00760 | 3.77772 | 3.32135 | 7.22932 | −1.00000 | −4.27308 | 6.04563 | −7.98348 | ||||||||||||||||||
1.7 | −2.39512 | 2.73656 | 3.73659 | −0.0657178 | −6.55437 | −1.00000 | −4.15933 | 4.48874 | 0.157402 | ||||||||||||||||||
1.8 | −2.35502 | −2.05082 | 3.54610 | −3.19924 | 4.82971 | −1.00000 | −3.64108 | 1.20585 | 7.53425 | ||||||||||||||||||
1.9 | −2.31087 | 1.67266 | 3.34013 | 2.25629 | −3.86530 | −1.00000 | −3.09688 | −0.202216 | −5.21401 | ||||||||||||||||||
1.10 | −2.24509 | −1.59687 | 3.04044 | 0.497524 | 3.58512 | −1.00000 | −2.33589 | −0.450015 | −1.11699 | ||||||||||||||||||
1.11 | −2.24499 | −3.23916 | 3.03997 | 1.71399 | 7.27186 | −1.00000 | −2.33471 | 7.49214 | −3.84789 | ||||||||||||||||||
1.12 | −2.16567 | −2.12383 | 2.69013 | −1.70035 | 4.59952 | −1.00000 | −1.49458 | 1.51067 | 3.68240 | ||||||||||||||||||
1.13 | −1.93646 | 1.74408 | 1.74988 | −0.828020 | −3.37734 | −1.00000 | 0.484346 | 0.0418063 | 1.60343 | ||||||||||||||||||
1.14 | −1.91984 | −0.598469 | 1.68580 | −2.87173 | 1.14897 | −1.00000 | 0.603223 | −2.64183 | 5.51328 | ||||||||||||||||||
1.15 | −1.83123 | −0.422202 | 1.35341 | 3.20494 | 0.773149 | −1.00000 | 1.18405 | −2.82175 | −5.86899 | ||||||||||||||||||
1.16 | −1.71301 | 0.519528 | 0.934389 | −1.00596 | −0.889955 | −1.00000 | 1.82540 | −2.73009 | 1.72321 | ||||||||||||||||||
1.17 | −1.71022 | −2.65285 | 0.924863 | −3.41231 | 4.53696 | −1.00000 | 1.83872 | 4.03760 | 5.83581 | ||||||||||||||||||
1.18 | −1.66695 | 2.04656 | 0.778727 | −1.41554 | −3.41151 | −1.00000 | 2.03580 | 1.18840 | 2.35964 | ||||||||||||||||||
1.19 | −1.59183 | 3.11735 | 0.533925 | −3.56187 | −4.96229 | −1.00000 | 2.33374 | 6.71786 | 5.66990 | ||||||||||||||||||
1.20 | −1.39424 | 1.76655 | −0.0561016 | 3.92427 | −2.46299 | −1.00000 | 2.86669 | 0.120703 | −5.47136 | ||||||||||||||||||
See all 66 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.c | ✓ | 66 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8029.2.a.c | ✓ | 66 | 1.a | even | 1 | 1 | trivial |