Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, 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("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.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: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
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 | −2.80428 | −1.04470 | 5.86401 | 3.49231 | 2.92963 | −4.86354 | −10.8358 | −1.90861 | −9.79343 | ||||||||||||||||||
1.2 | −2.66806 | 0.0181973 | 5.11854 | 3.52830 | −0.0485515 | 0.996923 | −8.32043 | −2.99967 | −9.41371 | ||||||||||||||||||
1.3 | −2.65443 | −2.20662 | 5.04598 | 0.185737 | 5.85731 | −3.52416 | −8.08534 | 1.86917 | −0.493026 | ||||||||||||||||||
1.4 | −2.63089 | 0.747844 | 4.92157 | 1.13408 | −1.96749 | 1.55238 | −7.68633 | −2.44073 | −2.98365 | ||||||||||||||||||
1.5 | −2.62862 | 3.02798 | 4.90963 | 2.24361 | −7.95940 | −3.55148 | −7.64830 | 6.16867 | −5.89760 | ||||||||||||||||||
1.6 | −2.62733 | 2.34750 | 4.90284 | −3.13713 | −6.16764 | −4.86517 | −7.62672 | 2.51073 | 8.24227 | ||||||||||||||||||
1.7 | −2.61377 | −0.423851 | 4.83180 | −1.13525 | 1.10785 | −2.59527 | −7.40168 | −2.82035 | 2.96728 | ||||||||||||||||||
1.8 | −2.59993 | −1.45421 | 4.75963 | −1.16680 | 3.78083 | 3.18169 | −7.17483 | −0.885282 | 3.03360 | ||||||||||||||||||
1.9 | −2.59547 | 1.19515 | 4.73648 | −3.51521 | −3.10198 | 1.20876 | −7.10244 | −1.57161 | 9.12363 | ||||||||||||||||||
1.10 | −2.57712 | −3.09746 | 4.64157 | −1.30860 | 7.98254 | 0.204481 | −6.80764 | 6.59427 | 3.37243 | ||||||||||||||||||
1.11 | −2.56362 | 2.58113 | 4.57213 | 0.513446 | −6.61703 | 0.254616 | −6.59395 | 3.66224 | −1.31628 | ||||||||||||||||||
1.12 | −2.54311 | 2.35643 | 4.46742 | −1.04349 | −5.99266 | 0.854661 | −6.27493 | 2.55275 | 2.65370 | ||||||||||||||||||
1.13 | −2.47232 | −2.46852 | 4.11238 | 2.27915 | 6.10297 | −3.16815 | −5.22247 | 3.09358 | −5.63478 | ||||||||||||||||||
1.14 | −2.31211 | −1.42285 | 3.34587 | 1.74031 | 3.28979 | 1.79626 | −3.11180 | −0.975501 | −4.02380 | ||||||||||||||||||
1.15 | −2.31178 | −3.06195 | 3.34432 | 1.34142 | 7.07855 | 1.68714 | −3.10776 | 6.37553 | −3.10106 | ||||||||||||||||||
1.16 | −2.27026 | −0.124315 | 3.15409 | 1.98639 | 0.282227 | 3.17086 | −2.62008 | −2.98455 | −4.50963 | ||||||||||||||||||
1.17 | −2.25257 | −2.81760 | 3.07408 | −4.05860 | 6.34684 | −4.96798 | −2.41944 | 4.93885 | 9.14228 | ||||||||||||||||||
1.18 | −2.25207 | 0.273415 | 3.07181 | −3.19262 | −0.615750 | −2.20872 | −2.41378 | −2.92524 | 7.19000 | ||||||||||||||||||
1.19 | −2.24392 | 1.38924 | 3.03516 | −1.50344 | −3.11734 | 0.570287 | −2.32282 | −1.07002 | 3.37359 | ||||||||||||||||||
1.20 | −2.22882 | 1.59395 | 2.96765 | 3.65354 | −3.55262 | −2.56474 | −2.15671 | −0.459333 | −8.14309 | ||||||||||||||||||
See next 80 embeddings (of 153 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(29\) | \(1\) |
\(277\) | \(1\) |
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 | 8033.2.a.b | ✓ | 153 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8033.2.a.b | ✓ | 153 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{153} + 3 T_{2}^{152} - 216 T_{2}^{151} - 649 T_{2}^{150} + 22810 T_{2}^{149} + 68641 T_{2}^{148} + \cdots - 2490304 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).