Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(143\) |
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 | −2.81318 | −2.25224 | 5.91397 | 2.72187 | 6.33595 | −2.92129 | −11.0107 | 2.07257 | −7.65711 | ||||||||||||||||||
1.2 | −2.73897 | −2.10858 | 5.50198 | −1.32967 | 5.77534 | 4.16128 | −9.59184 | 1.44610 | 3.64193 | ||||||||||||||||||
1.3 | −2.72223 | 2.61290 | 5.41054 | −3.36664 | −7.11292 | −3.38304 | −9.28427 | 3.82726 | 9.16478 | ||||||||||||||||||
1.4 | −2.70535 | −0.945977 | 5.31892 | 2.14258 | 2.55920 | −0.218411 | −8.97883 | −2.10513 | −5.79642 | ||||||||||||||||||
1.5 | −2.66984 | −0.755713 | 5.12803 | 0.937284 | 2.01763 | 2.29767 | −8.35133 | −2.42890 | −2.50240 | ||||||||||||||||||
1.6 | −2.65785 | 2.82218 | 5.06415 | 0.881121 | −7.50092 | 1.80840 | −8.14403 | 4.96471 | −2.34188 | ||||||||||||||||||
1.7 | −2.62887 | 1.58844 | 4.91095 | 0.705653 | −4.17581 | −0.559393 | −7.65249 | −0.476845 | −1.85507 | ||||||||||||||||||
1.8 | −2.59213 | 0.439138 | 4.71916 | 1.76571 | −1.13830 | 3.87571 | −7.04843 | −2.80716 | −4.57697 | ||||||||||||||||||
1.9 | −2.56363 | 3.26823 | 4.57221 | −1.87479 | −8.37854 | −1.87590 | −6.59421 | 7.68132 | 4.80627 | ||||||||||||||||||
1.10 | −2.54714 | −2.88541 | 4.48790 | −0.694174 | 7.34952 | −2.36870 | −6.33703 | 5.32557 | 1.76816 | ||||||||||||||||||
1.11 | −2.53949 | −2.72406 | 4.44903 | −2.80223 | 6.91773 | −4.07042 | −6.21931 | 4.42048 | 7.11625 | ||||||||||||||||||
1.12 | −2.53769 | 0.0556295 | 4.43986 | 2.89276 | −0.141170 | −5.18186 | −6.19160 | −2.99691 | −7.34093 | ||||||||||||||||||
1.13 | −2.48946 | −0.455224 | 4.19741 | −1.13104 | 1.13326 | −1.16006 | −5.47036 | −2.79277 | 2.81568 | ||||||||||||||||||
1.14 | −2.42374 | 0.415987 | 3.87452 | −3.49995 | −1.00824 | −1.51919 | −4.54334 | −2.82696 | 8.48296 | ||||||||||||||||||
1.15 | −2.40779 | 2.53147 | 3.79745 | 0.438044 | −6.09525 | 1.85360 | −4.32788 | 3.40834 | −1.05472 | ||||||||||||||||||
1.16 | −2.40357 | 1.04878 | 3.77713 | −2.29703 | −2.52082 | −0.387376 | −4.27144 | −1.90005 | 5.52106 | ||||||||||||||||||
1.17 | −2.32772 | −2.91674 | 3.41827 | 2.71745 | 6.78934 | 4.37081 | −3.30132 | 5.50736 | −6.32547 | ||||||||||||||||||
1.18 | −2.31697 | −3.13483 | 3.36836 | −3.69960 | 7.26332 | 1.63548 | −3.17044 | 6.82718 | 8.57187 | ||||||||||||||||||
1.19 | −2.31347 | 1.92997 | 3.35213 | 3.01701 | −4.46493 | −2.82894 | −3.12810 | 0.724803 | −6.97976 | ||||||||||||||||||
1.20 | −2.30190 | 0.450462 | 3.29874 | −0.676454 | −1.03692 | 2.59801 | −2.98957 | −2.79708 | 1.55713 | ||||||||||||||||||
See next 80 embeddings (of 143 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(23\) | \(-1\) |
\(349\) | \(-1\) |
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 | 8027.2.a.c | ✓ | 143 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8027.2.a.c | ✓ | 143 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{143} + 17 T_{2}^{142} - 59 T_{2}^{141} - 2603 T_{2}^{140} - 5067 T_{2}^{139} + \cdots + 167871723280 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).