Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(155\) |
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 | −2.80015 | 0.646146 | 5.84081 | 1.34449 | −1.80930 | 3.74304 | −10.7548 | −2.58250 | −3.76478 | ||||||||||||||||||
1.2 | −2.79202 | −1.96792 | 5.79536 | 4.22861 | 5.49445 | −4.72825 | −10.5967 | 0.872693 | −11.8064 | ||||||||||||||||||
1.3 | −2.78061 | −3.43962 | 5.73182 | −0.171450 | 9.56425 | −3.12589 | −10.3767 | 8.83098 | 0.476736 | ||||||||||||||||||
1.4 | −2.76736 | 2.97864 | 5.65827 | −2.08289 | −8.24297 | −3.08270 | −10.1238 | 5.87230 | 5.76411 | ||||||||||||||||||
1.5 | −2.76547 | 1.71486 | 5.64781 | −3.60382 | −4.74239 | −5.22895 | −10.0879 | −0.0592525 | 9.96624 | ||||||||||||||||||
1.6 | −2.74054 | −1.55820 | 5.51058 | −1.15483 | 4.27031 | −0.0750165 | −9.62090 | −0.572020 | 3.16485 | ||||||||||||||||||
1.7 | −2.73747 | 2.98404 | 5.49374 | −2.59125 | −8.16872 | 4.93159 | −9.56402 | 5.90448 | 7.09348 | ||||||||||||||||||
1.8 | −2.68312 | −1.89873 | 5.19916 | −4.03080 | 5.09454 | 2.89742 | −8.58374 | 0.605189 | 10.8151 | ||||||||||||||||||
1.9 | −2.67037 | −1.29029 | 5.13085 | 2.33945 | 3.44554 | 3.27756 | −8.36052 | −1.33516 | −6.24718 | ||||||||||||||||||
1.10 | −2.57631 | −2.78784 | 4.63739 | 0.760791 | 7.18234 | −2.92762 | −6.79473 | 4.77204 | −1.96004 | ||||||||||||||||||
1.11 | −2.57492 | 1.14041 | 4.63023 | 3.61279 | −2.93647 | −3.17107 | −6.77264 | −1.69947 | −9.30267 | ||||||||||||||||||
1.12 | −2.57220 | −0.502356 | 4.61621 | −1.32474 | 1.29216 | 1.13423 | −6.72941 | −2.74764 | 3.40751 | ||||||||||||||||||
1.13 | −2.52683 | 1.49048 | 4.38485 | −0.343930 | −3.76619 | 0.360206 | −6.02610 | −0.778467 | 0.869051 | ||||||||||||||||||
1.14 | −2.48799 | −3.03020 | 4.19010 | −2.87287 | 7.53911 | 1.28027 | −5.44894 | 6.18210 | 7.14768 | ||||||||||||||||||
1.15 | −2.47623 | 2.90051 | 4.13171 | 3.57414 | −7.18232 | −0.249825 | −5.27860 | 5.41293 | −8.85040 | ||||||||||||||||||
1.16 | −2.46916 | 1.70167 | 4.09677 | −3.39881 | −4.20171 | 3.51551 | −5.17727 | −0.104305 | 8.39223 | ||||||||||||||||||
1.17 | −2.45088 | 1.23773 | 4.00682 | 3.46965 | −3.03354 | −0.238635 | −4.91847 | −1.46802 | −8.50371 | ||||||||||||||||||
1.18 | −2.44945 | −0.158730 | 3.99982 | −2.39064 | 0.388803 | −3.35946 | −4.89848 | −2.97480 | 5.85577 | ||||||||||||||||||
1.19 | −2.44920 | −0.457827 | 3.99860 | −3.52685 | 1.12131 | −3.81804 | −4.89498 | −2.79039 | 8.63798 | ||||||||||||||||||
1.20 | −2.32032 | 0.985491 | 3.38390 | 2.02170 | −2.28666 | 0.848897 | −3.21110 | −2.02881 | −4.69101 | ||||||||||||||||||
See next 80 embeddings (of 155 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(71\) | \(-1\) |
\(113\) | \(-1\) |
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 | 8023.2.a.b | ✓ | 155 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8023.2.a.b | ✓ | 155 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{155} + 21 T_{2}^{154} - 10 T_{2}^{153} - 3250 T_{2}^{152} - 15745 T_{2}^{151} + 223779 T_{2}^{150} + \cdots - 4526112161 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).