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: | \(24\) |
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 | −2.65730 | 0 | 5.06126 | 0.532351 | 0 | 2.65721 | −8.13470 | 0 | −1.41462 | ||||||||||||||||||
1.2 | −2.65423 | 0 | 5.04495 | −4.31962 | 0 | −2.76583 | −8.08202 | 0 | 11.4653 | ||||||||||||||||||
1.3 | −2.58309 | 0 | 4.67235 | 0.467469 | 0 | −4.75978 | −6.90291 | 0 | −1.20751 | ||||||||||||||||||
1.4 | −2.57985 | 0 | 4.65561 | −1.47201 | 0 | 3.66706 | −6.85107 | 0 | 3.79756 | ||||||||||||||||||
1.5 | −2.12294 | 0 | 2.50689 | 0.133371 | 0 | 0.285383 | −1.07609 | 0 | −0.283139 | ||||||||||||||||||
1.6 | −2.08103 | 0 | 2.33067 | 3.72386 | 0 | −1.77284 | −0.688126 | 0 | −7.74944 | ||||||||||||||||||
1.7 | −1.94245 | 0 | 1.77311 | −4.08736 | 0 | 3.11287 | 0.440718 | 0 | 7.93949 | ||||||||||||||||||
1.8 | −1.42489 | 0 | 0.0303005 | 0.280637 | 0 | 2.09782 | 2.80660 | 0 | −0.399876 | ||||||||||||||||||
1.9 | −1.06967 | 0 | −0.855816 | −3.10564 | 0 | 2.58911 | 3.05477 | 0 | 3.32199 | ||||||||||||||||||
1.10 | −1.01887 | 0 | −0.961905 | −3.06877 | 0 | −4.42586 | 3.01779 | 0 | 3.12668 | ||||||||||||||||||
1.11 | −0.782084 | 0 | −1.38834 | 1.99725 | 0 | −0.182226 | 2.64997 | 0 | −1.56202 | ||||||||||||||||||
1.12 | −0.644697 | 0 | −1.58437 | 3.63356 | 0 | 1.88815 | 2.31083 | 0 | −2.34254 | ||||||||||||||||||
1.13 | −0.581479 | 0 | −1.66188 | −1.81978 | 0 | 1.51314 | 2.12931 | 0 | 1.05816 | ||||||||||||||||||
1.14 | 0.193256 | 0 | −1.96265 | 0.416886 | 0 | −3.71235 | −0.765807 | 0 | 0.0805657 | ||||||||||||||||||
1.15 | 0.358236 | 0 | −1.87167 | 0.906963 | 0 | 5.19227 | −1.38697 | 0 | 0.324907 | ||||||||||||||||||
1.16 | 0.427013 | 0 | −1.81766 | −3.85139 | 0 | −1.30591 | −1.63019 | 0 | −1.64459 | ||||||||||||||||||
1.17 | 1.06310 | 0 | −0.869811 | −1.32308 | 0 | −2.88846 | −3.05091 | 0 | −1.40657 | ||||||||||||||||||
1.18 | 1.16108 | 0 | −0.651891 | 2.55585 | 0 | −2.32357 | −3.07906 | 0 | 2.96755 | ||||||||||||||||||
1.19 | 1.39881 | 0 | −0.0433189 | −1.19656 | 0 | 1.89806 | −2.85822 | 0 | −1.67377 | ||||||||||||||||||
1.20 | 1.83794 | 0 | 1.37804 | 2.11982 | 0 | −1.32918 | −1.14313 | 0 | 3.89611 | ||||||||||||||||||
See all 24 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.c | ✓ | 24 |
3.b | odd | 2 | 1 | 4023.2.a.d | yes | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4023.2.a.c | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
4023.2.a.d | yes | 24 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 7 T_{2}^{23} - 12 T_{2}^{22} - 182 T_{2}^{21} - 105 T_{2}^{20} + 1953 T_{2}^{19} + \cdots - 375 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\).