Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, 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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
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 | −2.82403 | 0 | 5.97513 | 0.305598 | 0 | −1.90246 | −11.2259 | 0 | −0.863018 | ||||||||||||||||||
1.2 | −2.73865 | 0 | 5.50022 | −2.48832 | 0 | 2.47965 | −9.58588 | 0 | 6.81463 | ||||||||||||||||||
1.3 | −2.51871 | 0 | 4.34389 | 3.54254 | 0 | 3.81300 | −5.90358 | 0 | −8.92261 | ||||||||||||||||||
1.4 | −2.45057 | 0 | 4.00528 | −3.55507 | 0 | −0.769224 | −4.91408 | 0 | 8.71195 | ||||||||||||||||||
1.5 | −2.18150 | 0 | 2.75896 | −2.81097 | 0 | 0.316017 | −1.65567 | 0 | 6.13214 | ||||||||||||||||||
1.6 | −2.16693 | 0 | 2.69559 | −1.04157 | 0 | 3.90919 | −1.50729 | 0 | 2.25701 | ||||||||||||||||||
1.7 | −1.79652 | 0 | 1.22747 | 3.24604 | 0 | −3.00506 | 1.38786 | 0 | −5.83156 | ||||||||||||||||||
1.8 | −1.51618 | 0 | 0.298802 | 2.07566 | 0 | −1.53996 | 2.57932 | 0 | −3.14707 | ||||||||||||||||||
1.9 | −1.43306 | 0 | 0.0536673 | −2.81862 | 0 | −4.82450 | 2.78922 | 0 | 4.03925 | ||||||||||||||||||
1.10 | −1.23916 | 0 | −0.464485 | 0.602488 | 0 | 1.86008 | 3.05389 | 0 | −0.746578 | ||||||||||||||||||
1.11 | −0.964175 | 0 | −1.07037 | 0.686967 | 0 | −3.77336 | 2.96037 | 0 | −0.662356 | ||||||||||||||||||
1.12 | −0.614681 | 0 | −1.62217 | −3.33074 | 0 | 3.77407 | 2.22648 | 0 | 2.04734 | ||||||||||||||||||
1.13 | −0.305611 | 0 | −1.90660 | 1.63568 | 0 | −3.53407 | 1.19390 | 0 | −0.499884 | ||||||||||||||||||
1.14 | −0.0533591 | 0 | −1.99715 | 0.751347 | 0 | 2.49440 | 0.213285 | 0 | −0.0400912 | ||||||||||||||||||
1.15 | 0.365778 | 0 | −1.86621 | −3.76223 | 0 | −2.92149 | −1.41417 | 0 | −1.37614 | ||||||||||||||||||
1.16 | 0.530451 | 0 | −1.71862 | −3.35792 | 0 | 3.91494 | −1.97255 | 0 | −1.78121 | ||||||||||||||||||
1.17 | 0.599558 | 0 | −1.64053 | 0.261228 | 0 | −0.444015 | −2.18271 | 0 | 0.156622 | ||||||||||||||||||
1.18 | 0.680129 | 0 | −1.53742 | 2.78190 | 0 | −0.191226 | −2.40591 | 0 | 1.89205 | ||||||||||||||||||
1.19 | 1.30329 | 0 | −0.301424 | 3.35120 | 0 | −0.705123 | −2.99943 | 0 | 4.36761 | ||||||||||||||||||
1.20 | 1.35944 | 0 | −0.151922 | −3.36242 | 0 | 2.75034 | −2.92541 | 0 | −4.57100 | ||||||||||||||||||
See all 25 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(149\) | \(1\) |
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 | 4023.2.a.e | ✓ | 25 |
3.b | odd | 2 | 1 | 4023.2.a.f | yes | 25 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4023.2.a.e | ✓ | 25 | 1.a | even | 1 | 1 | trivial |
4023.2.a.f | yes | 25 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} + 7 T_{2}^{24} - 14 T_{2}^{23} - 196 T_{2}^{22} - 87 T_{2}^{21} + 2275 T_{2}^{20} + 3119 T_{2}^{19} + \cdots - 72 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\).