Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,2,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(4.36781699056\) |
Analytic rank: | \(0\) |
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 | −2.77274 | 2.24632 | 5.68811 | 3.59228 | −6.22846 | −1.86730 | −10.2262 | 2.04594 | −9.96049 | ||||||||||||||||||
1.2 | −2.25986 | −1.07595 | 3.10698 | −0.586151 | 2.43150 | 0.547575 | −2.50163 | −1.84234 | 1.32462 | ||||||||||||||||||
1.3 | −2.13103 | 0.778073 | 2.54127 | −1.92511 | −1.65809 | −4.90203 | −1.15346 | −2.39460 | 4.10246 | ||||||||||||||||||
1.4 | −2.06676 | −2.69874 | 2.27150 | 4.37160 | 5.57765 | 3.31581 | −0.561116 | 4.28320 | −9.03504 | ||||||||||||||||||
1.5 | −1.98290 | 2.22215 | 1.93190 | 0.712381 | −4.40631 | 4.39659 | 0.135039 | 1.93796 | −1.41258 | ||||||||||||||||||
1.6 | −1.71387 | −2.58580 | 0.937360 | 0.849164 | 4.43173 | −2.18891 | 1.82123 | 3.68636 | −1.45536 | ||||||||||||||||||
1.7 | −1.69494 | 3.21746 | 0.872829 | 1.65792 | −5.45340 | −0.657486 | 1.91049 | 7.35203 | −2.81008 | ||||||||||||||||||
1.8 | −1.12450 | 1.64314 | −0.735491 | 3.20489 | −1.84772 | −0.477395 | 3.07607 | −0.300096 | −3.60392 | ||||||||||||||||||
1.9 | −0.920985 | −0.533377 | −1.15179 | 1.81354 | 0.491232 | 3.82860 | 2.90275 | −2.71551 | −1.67024 | ||||||||||||||||||
1.10 | −0.240893 | −1.63498 | −1.94197 | −2.81730 | 0.393856 | −2.32432 | 0.949592 | −0.326830 | 0.678667 | ||||||||||||||||||
1.11 | −0.106981 | 0.649055 | −1.98856 | −2.10046 | −0.0694367 | 0.493203 | 0.426701 | −2.57873 | 0.224710 | ||||||||||||||||||
1.12 | 0.0847555 | −1.52830 | −1.99282 | 2.94110 | −0.129532 | −4.64869 | −0.338413 | −0.664306 | 0.249274 | ||||||||||||||||||
1.13 | 0.215054 | 2.12625 | −1.95375 | 4.42221 | 0.457259 | 1.19553 | −0.850270 | 1.52095 | 0.951013 | ||||||||||||||||||
1.14 | 0.253557 | 3.24523 | −1.93571 | −0.595274 | 0.822849 | 1.62460 | −0.997925 | 7.53151 | −0.150936 | ||||||||||||||||||
1.15 | 0.760071 | −2.84895 | −1.42229 | 3.94928 | −2.16541 | 1.21889 | −2.60119 | 5.11653 | 3.00173 | ||||||||||||||||||
1.16 | 0.814364 | 1.40134 | −1.33681 | 1.41612 | 1.14120 | 3.63098 | −2.71738 | −1.03623 | 1.15324 | ||||||||||||||||||
1.17 | 1.36387 | −2.44170 | −0.139855 | −1.90373 | −3.33016 | 2.23580 | −2.91849 | 2.96188 | −2.59645 | ||||||||||||||||||
1.18 | 1.73479 | 0.987380 | 1.00948 | 2.62354 | 1.71289 | −1.48197 | −1.71833 | −2.02508 | 4.55128 | ||||||||||||||||||
1.19 | 1.75045 | 3.07069 | 1.06407 | 3.05017 | 5.37508 | −4.64964 | −1.63830 | 6.42911 | 5.33917 | ||||||||||||||||||
1.20 | 1.98267 | 2.42262 | 1.93099 | −0.826438 | 4.80327 | 0.383471 | −0.136826 | 2.86911 | −1.63856 | ||||||||||||||||||
See all 25 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(547\) | \(-1\) |
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 | 547.2.a.c | ✓ | 25 |
3.b | odd | 2 | 1 | 4923.2.a.n | 25 | ||
4.b | odd | 2 | 1 | 8752.2.a.v | 25 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
547.2.a.c | ✓ | 25 | 1.a | even | 1 | 1 | trivial |
4923.2.a.n | 25 | 3.b | odd | 2 | 1 | ||
8752.2.a.v | 25 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} - 4 T_{2}^{24} - 30 T_{2}^{23} + 134 T_{2}^{22} + 365 T_{2}^{21} - 1926 T_{2}^{20} - 2226 T_{2}^{19} + \cdots + 8 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\).